I've tried to factor this for a long time but I can't get it right.

(x-2y)^3 + 4(2y-x)

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- May 4th 2008, 06:37 AMlax600Algebra - Factoring
I've tried to factor this for a long time but I can't get it right.

(x-2y)^3 + 4(2y-x) - May 4th 2008, 06:38 AMMoo
- May 4th 2008, 07:20 AMlax600
well the directions were for me to factor it completely. Since the problem was (x-2y)^3 + 4(2y - x). I figured I had to use one of those formulas. So at first I multiplied a -1 into (2y - x) to make it the same as the first part. Then it became (x - 2y)^3 + 4(2y - x). So I checked the answer, and it said the answer was:

(x - 2y)(x - 2y + 2)(x - 2y - 2)

So then I became confused... Like I don't see there's three -2y's and how the 2 and -2 from 4 went into the parenthesis.... yeah.. hehe - May 4th 2008, 07:33 AMMoo
No, when multiplying by -1, it may yield this :

$\displaystyle (x-2y)^3 + 4(2y - x)=(x-2y)^3-4(x-2y)$

$\displaystyle =(x-2y)\left((x-2y)^2-\underbrace{4}_{2^2}\right)$

Now, do you know the formula : $\displaystyle a^2-b^2=(a-b)(a+b)$ ? - May 4th 2008, 07:38 AMlax600
yeah i know that formula... heh.. forgot that I had to multiply the 4 by -1 too.