# Thread: factoring is confusing me. help...

1. ## factoring is confusing me. help...

i really need help with some factoring!!
ive been working on these 2 problems foreverrr!!!!!!!!!!

(x+a)^2 - 2(x+a) (y+a) + (y+a)^2

and

x^2-8x(x-3y) +16(x-3y)^2

2. Hi xosherry,

For the first problem,
$\displaystyle (x+a)^2 -2(x-a)(y+a) +(y+a)^2$

try a change of variables to maybe simplify things
let $\displaystyle u=(x+a) \; v=(y+a)$ then rewriting the equation results in

$\displaystyle u^2-2uv+v^2 \ { } = \ { } (u-v)(u-v)=(u-v)^2$

now replacing what we defined as u and v we get

$\displaystyle [ (x+a)-(y+a)]^2 \;=[x+a-y-a]^2 =(x-y)^2$

For the second problem $\displaystyle x^2 -8x(x-3y) +16(x-3y)^2$

using the same technique let $\displaystyle u=x \; v=(x-3y)$
rewriting the equation will result in

$\displaystyle u^2 -8uv-16v^2$

factor this expression and back substitute for u and v

Hope this helps

3. Originally Posted by Nokio720
Hi xosherry,

For the first problem,
$\displaystyle (x+a)^2 -2(x\color{red}+\color{black}a)(y+a) +(y+a)^2$

try a change of variables to maybe simplify things

Hope this helps
A very tiny typo
Just remember the formula he has given