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

2 Answers
Apr 22, 2018

Answer:

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

Explanation:

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

Apr 22, 2018

Answer:

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)#