# Thread: Factoring help

1. ## Factoring help

How do you factor
(a+b)^2-(2a-b)^2
and
(a+b)^2-4(b+c)^2
without simplifying the expression?

2. Originally Posted by sinjid9
How do you factor
(a+b)^2-(2a-b)^2
and
(a+b)^2-4(b+c)^2
without simplifying the expression?
Each of them is a difference of two squares.

Remember that $(x + y)(x - y) = x^2 - y^2$.

$(a + b)^2 - (2a - b)^2 = [(a + b) + (2a - b)][(a + b) - (2a - b)]$

$= 3a(2b - a)$.

$(a+b)^2-4(b+c)^2 = (a + b)^2 - [2(b + c)]^2$

$= (a + b)^2 - (2b + 2c)^2$

$= [(a + b) + (2b + 2c)][(a + b) - (2b + 2c)]$

$= (a + 3b + 2c)(a - b - 2c)$.

3. Originally Posted by sinjid9
How do you factor
(a+b)^2-(2a-b)^2
and
(a+b)^2-4(b+c)^2
without simplifying the expression?
(a+b)^2-(2a-b)^2 is in the form of $x^2-y^2$ where x = a+b and y = (2a-b)

you should know that $a^2-b^2=(a-b)(a+b)$

4. Thanks for the help, both of you.