Thread: polynomial

I'm asked to simplify

(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

Originally Posted by reallylongnickname

I'm asked to simplify

(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.
, not

-Dan

Since it can be rewritten as

This gives an equation of the form so you can use the difference of two squares.

An alternative method is the one highlighted above

(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.

Originally Posted by reallylongnickname

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

isn't It is

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.

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

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?

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