1. ## polynomial

(x+2)^2 (x-1)^2 - (x-4)^2 (x+4)^2

something is wrong with this x^2 +4x +4 +x^2 - 1 -x^2 +16 +x^2 +8x +16

2. Originally Posted by reallylongnickname

(x+2)^2 (x-1)^2 - (x-4)^2 (x+4)^2

something is wrong with this x^2 +4x +4 +x^2 - 1 -x^2 +16 +x^2 +8x +16
First, you are expanding out the individual terms, but you aren't multiplying them.

(x^2 +4x +4) + (x^2 - 1) - (x^2 +16) + (x^2 +8x +16)

Second you are not squaring these right.
$\displaystyle (x - 1)^2 = x^2 - 2x + 1$, not $\displaystyle x^2 -1$

-Dan

3. Since $\displaystyle a^2b^2 = (ab)^2$ it can be rewritten as $\displaystyle ((x+2)(x-1))^2 - ((x-4)(x+4))^2$

This gives an equation of the form $\displaystyle a^2-b^2$ so you can use the difference of two squares.

An alternative method is the one highlighted above

4. (x^2 +4x +4) (x^2 -2x -1) - (x^2 +16) (x^2 +8x +16)

-x^2 -16 (x^2 +8x +16)

-x^4 -8x^3 -16x^2 -16x^2 -128x -256

x^4 -2x^3 -x^2 + 4x^3 -8x -4x +4x^2 -8x -4 -x^2 - 16 -x^4 -8x^3 -16x^2 -16x^2 -128x -256

It's not finished yet I know. Once I started collecting like terms, I notice something was done wrong.

5. Originally Posted by reallylongnickname
(x^2 +4x +4) (x^2 -2x -1) - (x^2 +16) (x^2 +8x +16)
$\displaystyle (x-4)^2$ isn't $\displaystyle (x^2+16)$ It is $\displaystyle x^2 - 8x +16$

6. For the 2nd part: -(x^2 -8x +16) (x^2 +8x +16)
I came up with: -x^2 +8x -16 (x^2 +8x +16)
then: -x^2 _8x^3 -16x^2 + 8x^3 + 64x^2 +128x -16^2 -128x -256

Still doing something wrong.

7. Originally Posted by reallylongnickname
For the 2nd part: -(x^2 -8x +16) (x^2 +8x +16)
I came up with: -x^2 +8x -16 (x^2 +8x +16)
then: -x^2 _8x^3 -16x^2 + 8x^3 + 64x^2 +128x -16^2 -128x -256

Still doing something wrong.
You have it. Just collect like terms.

-Dan

8. The answer I came up with is: 2x^3 +25x^2 -252 The correct answer is apparently:
2x^3 +29x^2 -4x -252

By the way, where does everyone get the application to nicely display math work like that?

9. Originally Posted by reallylongnickname
The answer I came up with is: 2x^3 +25x^2 -252 The correct answer is apparently:
2x^3 +29x^2 -4x -252

By the way, where does everyone get the application to nicely display math work like that?
Yes, that is correct!

For the LaTeX codes, see here.

-Dan