How do you factor (9a+3b-c)^2-(3a-2b+c)^2 ?

2 Answers
Apr 22, 2018

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

Explanation:

Using that will give you (6a+5b-2c)(12a+b)

Apr 22, 2018

Using the difference of two squares, we get (12 a + b)(6a+5b-2c).

Explanation:

In general the difference of two squares factors easily:

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

(9a+3b-c)^2-(3a-2b+c)^2

= (9a + 3b -c + 3a -2b +c)(9a + 3b -c - 3a +2b -c)

= (9a + 3b -c + 3a -2b +c)(9a + 3b -c - 3a +2b -c)

= (12 a + b)(6a+5b-2c)