Up until today, I've always considered the following expression:
-x^2 = x^2
thinking that -x is one term, that when squared, is always positive. But in fact, I've recently discovered -x represents two terms:
-x = (minus) (1)(x)
NOT
-x = (negative x)
where x is subtracted from an assumed 0. Therefore:
-x = (0) - (1)(x)
From this theorem (is this a theorem?), then expressions such as:
-3^2 = -9 == -(3)^2 = -9
Reads as: (assumed zero) minus the square of three equals negative nine
OR
Reads as: the square of three subtracted (from an assumed zero) equals negative nine
The logical flow is: three is squared and then the opposite is found. the result is a negative nine
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
The above leads into an actual problem I worked on for algebra.
Determine if the point (-2, 2) passes through the line x^2 + y^2 = 4
The expression x^2 + y^2 = 4 is equivalent to the following expressions:
y^2 = -x^2 + 4
-y^2 = x^2 - 4
x^2 + y^2 - 4 = 0
The answers for each equivalent expression, plugging in point (-2, 2) are as follows (in order of expressions shown above):
x^2 + y^2 = 4
(-2)^2 + (2)^2 = 4
4 + 4 = 4
8 != 4 // this is the book's answer
y^2 = -x^2 + 4
(2)^2 = -(-2)^2 + 4
4 = -4 + 4
4 != 0
-y^2 = x^2 - 4
-(2)^2 = (-2)^2 - 4
-4 = 4 - 4
-4 != 0
x^2 + y^2 - 4 = 0
(-2)^2 + (2)^2 - 4 = 0
4 + 4 - 4 = 0
8 - 4 = 0
8 != 4 OR 4 != 0
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
What started all this confusion for me, was I converted x^2 + y^2 = 4 into slope-intercept form (out of habit) of y^2 = -x^2 + 4 and as shown above, my answer of 4 != 0 did not match the book's answer, which really threw me off.
It has taken me about a full day to understand and be able to define what -x^2 actually means.
0 - (1)(0 + x)^2
Anyone else encounter frustration like this? besides any frustration you may have reading reading this post or trying to understand it.
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Yeah when i first got into college, i was thrown by the "there are no negative numbers, only (negative) * number. But that's about it.
there is a basic flaw in your theorum which is throwing you off.
-3^2 = 9
-(3^2) = -9
-3 does imply 0-3. But a negative number multiplied by a negative number (as in the case of -3^2) will always equal a positive.
if you were to apply the second form of the equation THAT is when you would be assuming that the answer is 0 - 3^2, or 0 - 9 and therefor -9.
The key is the addition of parenthesis to imply logic to the equation. both of the above equationas are correct. There is a rule in mathmatics that requires you first address what is contained in parenthesis and then apply anything outside of them.
Your confusions is simply a matter of misunderstanding the rules.
In your example from the text:
-2^2 = 4
-(2^2) = -4
The second is NOT correct as it would require the original equation read -(x^2) + y^2 = 4, which it does not.
That is why your answer differed from the one in the book. As usual, the book is right ;)
I hope I explained this well enough >.>
Edited, Sat Jan 22 14:03:41 2005 by fetichwon
-3^2 = 9
-(3^2) = -9
-3 does imply 0-3. But a negative number multiplied by a negative number (as in the case of -3^2) will always equal a positive.
if you were to apply the second form of the equation THAT is when you would be assuming that the answer is 0 - 3^2, or 0 - 9 and therefor -9.
The key is the addition of parenthesis to imply logic to the equation. both of the above equationas are correct. There is a rule in mathmatics that requires you first address what is contained in parenthesis and then apply anything outside of them.
Your confusions is simply a matter of misunderstanding the rules.
In your example from the text:
Quote:
Determine if the point (-2, 2) passes through the line x^2 + y^2 = 4
-2^2 = 4
-(2^2) = -4
The second is NOT correct as it would require the original equation read -(x^2) + y^2 = 4, which it does not.
That is why your answer differed from the one in the book. As usual, the book is right ;)
I hope I explained this well enough >.>
Edited, Sat Jan 22 14:03:41 2005 by fetichwon
Quote:
-2^2 = 4
-(2^2) = -4
The second is NOT correct as it would require the original equation read -(x^2) + y^2 = 4, which it does not.
-(2^2) = -4
The second is NOT correct as it would require the original equation read -(x^2) + y^2 = 4, which it does not.
I once thought this as well, but I can give examples that state otherwise.
To test using a calculator (TI-83), enter the expression -3^2 and your answer WILL be -9.
This implies that there is an implied parentheses where the minus operator is outside the parentheses. Now, it could very well be that it should read as -(3^2) = -9 instead of -(3)^2 = -9, this is just a semantic difference in my lack of understanding on the use of parentheses, but is ultimately moot with respect to the actual issue at hand.
In my Algebra Review book, an example given reads as:
Edit#3 (and Edit#4. minor correction for sake of consistency; changed 0-1(0-3)^0 to 0-1(0+3)^2.) Edit#5. more changes for sake of consistency; changed (0-3)^0 to ((0-1)(0+3))^0
Quote:
(example b) (-3)^0 = 1
// this seems to be the same as: ((0-1)(0+3))^0 = 1
(example d) -3^0 = -1
// this seems to be the same as: 0-1(0+3)^0 = -1
// this seems to be the same as: ((0-1)(0+3))^0 = 1
(example d) -3^0 = -1
// this seems to be the same as: 0-1(0+3)^0 = -1
The book uses the explanation: in part (d), 3 is raised to the power of 0, and then we find the opposite of 1 to get -1.
Doesn't this imply the use of parentheses? Since, I would think it to be a natural assumption to say -3 = negative three, but as Barretboy pointed out, this is not correct. There are no negative numbers, only (negative) * (number)... Edit#2 or as I'm starting to think of it as, (zero minus number).
Edit: Tested with TI-83 calculator
Quote:
-2^2 = -4
-(2^2) = -4
-(2^2) = -4
Edited, Sat Jan 22 14:53:07 2005 by tchzarmok
Edited, Sat Jan 22 14:58:36 2005 by tchzarmok
Edited, Sat Jan 22 15:13:39 2005 by tchzarmok
Edited, Sat Jan 22 16:17:45 2005 by tchzarmok
Edited, Sat Jan 22 16:22:22 2005 by tchzarmok
http://ffxi.allakhazam.com/uf/Kelvyquayo/explhead.gif
my thoughts exactly Kelv
laugh my a** off
tchzarmok wrote:
Quote:
-2^2 = 4
-(2^2) = -4
The second is NOT correct as it would require the original equation read -(x^2) + y^2 = 4, which it does not.
-(2^2) = -4
The second is NOT correct as it would require the original equation read -(x^2) + y^2 = 4, which it does not.
I once thought this as well, but I can give examples that state otherwise.
To test using a calculator (TI-83), enter the expression -3^2 and your answer WILL be -9.
I don't have a calculator :(
tchzarmok wrote:
This implies that there is an implied parentheses where the minus operator is outside the parentheses. Now, it could very well be that it should read as -(3^2) = -9 instead of -(3)^2 = -9, this is just a semantic difference in my lack of understanding on the use of parentheses, but is ultimately moot with respect to the actual issue at hand.
Well the whole point of parenthesis in formula's is to guide you as to what needs to be done first. Therefore this is a waste of your parenthesis as there is nothing to DO with a simple integer.
tchzarmok wrote:
In my Algebra Review book, an example given reads as:
Edit#3
The book uses the explanation: in part (d), 3 is raised to the power of 0, and then we find the opposite of 1 to get -1.
Doesn't this imply the use of parentheses? Since, I would think it to be a natural assumption to say -3 = negative three, but as Barretboy pointed out, this is not correct. There are no negative numbers, only (negative) * (number)... Edit#2 or as I'm starting to think of it as, (zero minus number).
Edit#3
Quote:
(example b) (-3)^0 = 1
// this seems to be the same as: (0-3)^0 = 1
(example d) -3^0 = -1
// this seems to be the same as: 0-1(0-3)^0 = -1
// this seems to be the same as: (0-3)^0 = 1
(example d) -3^0 = -1
// this seems to be the same as: 0-1(0-3)^0 = -1
The book uses the explanation: in part (d), 3 is raised to the power of 0, and then we find the opposite of 1 to get -1.
Doesn't this imply the use of parentheses? Since, I would think it to be a natural assumption to say -3 = negative three, but as Barretboy pointed out, this is not correct. There are no negative numbers, only (negative) * (number)... Edit#2 or as I'm starting to think of it as, (zero minus number).
Edit: Tested with TI-83 calculator
Quote:
-2^2 = -4
-(2^2) = -4
-(2^2) = -4
No calculator, no algebra book! I'm working blind here!
There are several different ways to set up the equation:
(-3)^2 = 9
Here you are squaring a "negative" number. Negative multiplied by negative is positive, so that equation is accurate.
-(3^2) = -9
Here you are subtracting a sum (3^2) from zero, resulting in a negative number. This equation is also accurate.
-3^2 = 9 or -3^2 = -9
The problem here is there are no parentheses guiding the order of your calculations. Theoretically, as per the rule about order of calcuations, you multiply before you subtract. If you are seeing each symbol as separate then yes, the answer SHOULD be -9.
Multiply first = 3^2
Then subtract = -9
I concede I was wrong in my original post, but I blame it on the fact that the last algebra class I took was in 1994.
when you type - 3 ^ 2 into the ti 83, it's giving you -9 for precisely one reason: powers, multiplication, division, etc, all take precedence over addition/subtraction, so it takes the last part (3 ^ 2), and gets 9. then it does 0-9 to find -9
try 3 - 2 * 2 and figure out if you get 2 (1 * 2), or -1 (3 - 4). i assure you the latter, for the same reason you get -9 above.
in a case where you actually have variables, such that x = -2, y = 2, and you want to find x ^ 2 and y ^ 2, there is no opportunity for raising to the power "before" you do the subtraction. when you substitute in the values into x ^ 2, you're getting (-2) ^ 2, simply because a variable IS a value, not just a text replacement.
i'm not sure if the ti83, specifically, allows you to define variables, etc. But if you get a ti85, ti89, etc, you can define x as -2, then see what it gives you for x ^2. i assure you it will be 4, not -4.
try 3 - 2 * 2 and figure out if you get 2 (1 * 2), or -1 (3 - 4). i assure you the latter, for the same reason you get -9 above.
in a case where you actually have variables, such that x = -2, y = 2, and you want to find x ^ 2 and y ^ 2, there is no opportunity for raising to the power "before" you do the subtraction. when you substitute in the values into x ^ 2, you're getting (-2) ^ 2, simply because a variable IS a value, not just a text replacement.
i'm not sure if the ti83, specifically, allows you to define variables, etc. But if you get a ti85, ti89, etc, you can define x as -2, then see what it gives you for x ^2. i assure you it will be 4, not -4.
tchzarmok wrote:
To test using a calculator (TI-83), enter the expression -3^2 and your answer WILL be -9.
That is because you are not puting the numbers in to the calulator with a correct syntax.
Let me introduce you to a friend I like to call "The order of operations" I would assume that you understand the order of operations, but you have to realize that your calculator has a raging hard-on for it.
So when you put in -3^2, it will compute that as (-1)(3^2)=-9.
If you put in (-3)^2 however, you will get the answer to be 9.
Chech out pg. 9 It talks about Order of Ops. (pdf)
Quote:
If you are seeing each symbol as separate...
That was my problem. I was seeing -3 as a single term, like x^2 = 9, x = 3 OR x = -3.
Whereas -3 is: zero minus three.
Quote:
in a case where you actually have variables, such that x = -2, y = 2, and you want to find x ^ 2 and y ^ 2, there is no opportunity for raising to the power "before" you do the subtraction.
quoted for emphasis. I agree ;)
Quote:
That is because you are not puting the numbers in to the calulator with a correct syntax.
I'm relating examples from a textbook. -3^0 = -1 is a specific example which triggered this whole thing.
I understand now, and prior to this thread, that when x = -3:
x^0 = 1
and
-3^0 = -1
My point of this thread was that, -3 is actually short-hand for (0 - 3) since there are no parenthesis declaring an order of operations.
Edit: I just realized, -3 is more like 0 - 3, not (0 - 3), since the parenthesis would force it to occur first. Rather than edit each post of every instance of (0 - 3), I was using it to convey 0 - 3. Thanks for the replies and sharing your thoughts.
Edited, Sat Jan 22 17:24:01 2005 by tchzarmok
t('-'t )
Bode - 100 Holy Paladin - Lightbringer
I dont think 0-3 is how it is figured. It is more of a -1*3^2=-9. It has been a while, but I remember several different problems had implied a - sign as a -1, but usually invoved parenthesis as well.
tzam.. the guy who made the thread wrote:
The expression x^2 + y^2 = 4 is equivalent to the following expressions:
y^2 = -x^2 + 4
-y^2 = x^2 - 4
x^2 + y^2 - 4 = 0
The answers for each equivalent expression, plugging in point (-2, 2) are as follows (in order of expressions shown above):
x^2 + y^2 = 4
(-2)^2 + (2)^2 = 4
4 + 4 = 4
8 != 4 // this is the book's answer
y^2 = -x^2 + 4
-y^2 = x^2 - 4
x^2 + y^2 - 4 = 0
The answers for each equivalent expression, plugging in point (-2, 2) are as follows (in order of expressions shown above):
x^2 + y^2 = 4
(-2)^2 + (2)^2 = 4
4 + 4 = 4
8 != 4 // this is the book's answer
I think I just pissed myself, can I get some paper?
I just had a meltdown with respect to the whole -x^2 thing. I thought I understood it... I really did. But I don't. Looking over other particular problems tends to conflict with the way I think -x^2 should work. I will be getting help in my college math center, but also will explain what I mean to anyone interested. Maybe I'm overlooking something (probably am) or maybe I've found specific references in different problems, using equivalent expressions to obtain different results.
So, first I will quote problems (not many) within my Algebra Review book and College Algebra book, to provide a framework to reference everything by.
Much of the following will be a regurgitation, but an orderly regurgitation.
List the intercepts and test for symmetry, for the line x^2 + y - 9 = 0.
y = -x^2 + 9
y-intercept: (0,9)
x-intercepts: (3,0) and (-3,0)
Testing y-axis symmetry
-x^2 + y - 9 = 0
y - 9 = x^2
y = x^2 + 9 // the book says this is equivalent to y = -x^2 + 9
// and therefore, this line is symmetrical to the y-axis
The book is indirectly stating that x^k = -x^k = x^k
which states that -x^k = (-x)^k, where k is a non-negative integer. But according to Algebra Review, parts (b) and (d), -x^k != (-x)^k.
Without parenthesis, order of operations dictates that x is raised to the power k prior to being subtracted from an assumed zero or multiplied by an assumed negative one.
Order of operations is crucial, to say the least. And is assumed in other areas of math. Such as, numerator and denominator. Fractions are assumed to have parentheses around the numerator and denomenator, even if it is not written as such, and only varies if parentheses are written in a particular order.
Example 8
Evaluate:
22 + 8
------
8 + 2
"...we treat this expression as if parentheses enclose the numerator and the denomenator."
So, 22+8/8+2 = (22+8)/(8+2) even though it's not written as such. Without the parentheses, the problem becomes, "22 + 8 / 8 + 2 = 25."
An example on the next page treats -4^2 as -(4^2) even though it is written without parentheses. And you make ask, so what? -4^2 IS the same as -(4^2). BUT if 4 were negative... -4^2 != -(-4^2) because -(-4^2) => -(- 4 * 4) => -(-16) => +16. -4^2 != +16
I tried to find a problem that showed a negative variable being squared, such as -x^2, where x = negative integer. I wanted to find proof that plugging in the negative integer results in parentheses placed as such, "-(-2^2)." If I could show that this is how the book handles plugging in negative integers into negative variables, then I can prove how it conflicts with: x^2 = -x^2 = x^2.
Again, I will be addressing this with the math department, but also wanted to share this... infinite frustration I have developed. I'll never look at the square of a negative variable the same again.
Edit: minor fixes, for clarification
Edited, Sun Jan 23 00:45:53 2005 by tchzarmok
Edited, Sun Jan 23 01:01:04 2005 by tchzarmok
So, first I will quote problems (not many) within my Algebra Review book and College Algebra book, to provide a framework to reference everything by.
Much of the following will be a regurgitation, but an orderly regurgitation.
"Algebra Review: Laws of Exponents" wrote:
Example 8
(b) (-3)^0 = 1
(d) -3^0 = -1
In part (b), -3 is raised to the 0 power, giving the answer 1; in part (d), 3 is raised to the 0 power to get 1, and then we find the opposite of 1 to get -1.
(b) (-3)^0 = 1
(d) -3^0 = -1
In part (b), -3 is raised to the 0 power, giving the answer 1; in part (d), 3 is raised to the 0 power to get 1, and then we find the opposite of 1 to get -1.
"Algebra Problem: Case Study 01" wrote:
List the intercepts and test for symmetry, for the line x^2 + y - 9 = 0.
y = -x^2 + 9
y-intercept: (0,9)
x-intercepts: (3,0) and (-3,0)
Testing y-axis symmetry
-x^2 + y - 9 = 0
y - 9 = x^2
y = x^2 + 9 // the book says this is equivalent to y = -x^2 + 9
// and therefore, this line is symmetrical to the y-axis
The book is indirectly stating that x^k = -x^k = x^k
which states that -x^k = (-x)^k, where k is a non-negative integer. But according to Algebra Review, parts (b) and (d), -x^k != (-x)^k.
Without parenthesis, order of operations dictates that x is raised to the power k prior to being subtracted from an assumed zero or multiplied by an assumed negative one.
Order of operations is crucial, to say the least. And is assumed in other areas of math. Such as, numerator and denominator. Fractions are assumed to have parentheses around the numerator and denomenator, even if it is not written as such, and only varies if parentheses are written in a particular order.
"Algebra Review: Numbers and their properties" wrote:
Example 8
Evaluate:
22 + 8
------
8 + 2
"...we treat this expression as if parentheses enclose the numerator and the denomenator."
So, 22+8/8+2 = (22+8)/(8+2) even though it's not written as such. Without the parentheses, the problem becomes, "22 + 8 / 8 + 2 = 25."
An example on the next page treats -4^2 as -(4^2) even though it is written without parentheses. And you make ask, so what? -4^2 IS the same as -(4^2). BUT if 4 were negative... -4^2 != -(-4^2) because -(-4^2) => -(- 4 * 4) => -(-16) => +16. -4^2 != +16
I tried to find a problem that showed a negative variable being squared, such as -x^2, where x = negative integer. I wanted to find proof that plugging in the negative integer results in parentheses placed as such, "-(-2^2)." If I could show that this is how the book handles plugging in negative integers into negative variables, then I can prove how it conflicts with: x^2 = -x^2 = x^2.
Again, I will be addressing this with the math department, but also wanted to share this... infinite frustration I have developed. I'll never look at the square of a negative variable the same again.
Edit: minor fixes, for clarification
Edited, Sun Jan 23 00:45:53 2005 by tchzarmok
Edited, Sun Jan 23 01:01:04 2005 by tchzarmok
when multiplying anyting to a power keep in mind the (-) at the beinging will always imply a -1 multiplyed by the number you are multipying.
there for a:
-1(3)^2 will always = a -9
the only way around this is with an absolute value of -1 witch always = 1 in which case:
/-1/(3)^2 = 9 this is where you are having a problem.
there for a:
-1(3)^2 will always = a -9
the only way around this is with an absolute value of -1 witch always = 1 in which case:
/-1/(3)^2 = 9 this is where you are having a problem.
hmmm... Maybe when it's not midnight I'll give that another read through. Interesting from what I did get to though.
Quote:
when multiplying anyting to a power keep in mind the (-) at the beinging will always imply a -1 multiplyed by the number you are multipying.
I really want to believe that. but I can't when my book allows the following:
Quote:
y = x^2 + 9 // the book says this is equivalent to y = -x^2 + 9
// and therefore, this line is symmetrical to the y-axis
// and therefore, this line is symmetrical to the y-axis
Quote:
Again, I will be addressing this with the math department, but also wanted to share this... infinite frustration I have developed. I'll never look at the square of a negative variable the same again.
And yet, somehow, the world continues to spin on its axis.
Quote:
And yet, somehow, the world continues to spin on its axis.
shrodinger's cat got out of the box (yes, IT'S ALIVE) and is chasing hamsters around the world, from inside it of course. the result is a spinning world on it's axis. i thawt every1 knew that
Call me crazy, but maybe I'm figuring it out again. And will maybe have another relapse also.
-x^2 = (-x)^2
It cannot equal (-x^2) or the number will be squared before multiplied by negative 1. It cannot equal -(x)^2 because the number will be squared before multiplied by negative 1, and would also make the statement -x^2 != x^2 (which is false).
However, the parentheses placement is different for an integer than a variable term. Consider,
-3^0 = -1
This means, -(3^0) = -1. Specific book examples show that other integer terms when squared, are similar. -4^2 = -(4^2) for example.
-x = (-x)
-3 = -(3)
I don't yet understand why, but this resolves all conflicts I've had.
-x^2 = (-x)^2
It cannot equal (-x^2) or the number will be squared before multiplied by negative 1. It cannot equal -(x)^2 because the number will be squared before multiplied by negative 1, and would also make the statement -x^2 != x^2 (which is false).
However, the parentheses placement is different for an integer than a variable term. Consider,
-3^0 = -1
This means, -(3^0) = -1. Specific book examples show that other integer terms when squared, are similar. -4^2 = -(4^2) for example.
-x = (-x)
-3 = -(3)
I don't yet understand why, but this resolves all conflicts I've had.
Tchzarmok and Jerod
at Tinagra
where the walls fell.
don't ask..
at Tinagra
where the walls fell.
don't ask..
that was a cool st:ng episode
Guys. A minus sign means that you multiply a "-1" by the element the minus sign applies to.
Remember the orders though. You multply first. You should always think of any expression as a series of added multiplications.
So if you've got an expression like 3xy4z+5xz^2-3x^2, the very first thing you do is break up each of the sections by where the + or - signs are. That gives you three:
3xy4z
+
5xz^2
+ (replace minus sign with plus sign since subtraction is just adding a negative number, and this will make equation manipulation 100 times easier)
(-1)3x^2
When multiplying out each section, remember that the multiplications can be done in *any* order. It does not matter if it's 3*x*y*4*z, or x*3*z*4*y. They are *exactly* the same expression. Simply multiply them together. In the first expression, we get 12*x*y*z. Note, that we can adjust this at will. If we need to cancel out a 6 in another part of the equation, we could transform the 3*4 into 2*6, then cancel the 6 and end up with 2xyz as the final expression. That's what algebra is about. That's what you're supposed to be picking up.
Also remember that exponents are just more multiplication. The second expression is actually 5*x*z*z. That's it. Nothing more complicated then that. If you had a z to cancel out for some reason, you can simply cross off one of the z's in this part and end up with 5xz (or any other ordering of those units).
The last one is treated the same. The expression is -1*3*x*x. If x was equal to "2", then the result would be -12.
Note that exponents are a higher order. If we'd expressed that as (3x)^2, then the exponent would apply to the entire expression in the parenthesis. Once again though we just multiply them. The result is 3*x*3*x. IIRC, a -(3x)^2 would resolve to -1*3*x*3*x, wheras a (-3x)^2 would resolve to -1*3*x*-1*3*x (you're just taking (-1*3*x)*(-1*3*x) right?).
Follow those rules, and algebra becomes pretty darn easy...
Remember the orders though. You multply first. You should always think of any expression as a series of added multiplications.
So if you've got an expression like 3xy4z+5xz^2-3x^2, the very first thing you do is break up each of the sections by where the + or - signs are. That gives you three:
3xy4z
+
5xz^2
+ (replace minus sign with plus sign since subtraction is just adding a negative number, and this will make equation manipulation 100 times easier)
(-1)3x^2
When multiplying out each section, remember that the multiplications can be done in *any* order. It does not matter if it's 3*x*y*4*z, or x*3*z*4*y. They are *exactly* the same expression. Simply multiply them together. In the first expression, we get 12*x*y*z. Note, that we can adjust this at will. If we need to cancel out a 6 in another part of the equation, we could transform the 3*4 into 2*6, then cancel the 6 and end up with 2xyz as the final expression. That's what algebra is about. That's what you're supposed to be picking up.
Also remember that exponents are just more multiplication. The second expression is actually 5*x*z*z. That's it. Nothing more complicated then that. If you had a z to cancel out for some reason, you can simply cross off one of the z's in this part and end up with 5xz (or any other ordering of those units).
The last one is treated the same. The expression is -1*3*x*x. If x was equal to "2", then the result would be -12.
Note that exponents are a higher order. If we'd expressed that as (3x)^2, then the exponent would apply to the entire expression in the parenthesis. Once again though we just multiply them. The result is 3*x*3*x. IIRC, a -(3x)^2 would resolve to -1*3*x*3*x, wheras a (-3x)^2 would resolve to -1*3*x*-1*3*x (you're just taking (-1*3*x)*(-1*3*x) right?).
Follow those rules, and algebra becomes pretty darn easy...
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