How do you factor 36a ^ { 2} - 36a b - 27b ^ { 2}36a236ab27b2?

2 Answers
May 19, 2017

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

Explanation:

Given, 36a^2-36ab-27b^2 = 9(4a^2-4ab-3b^2)36a236ab27b2=9(4a24ab3b2)

rArr 9(4a^2-6ab+2ab-3b^2)9(4a26ab+2ab3b2)

rArr 9[2a(2a-3b)+b(2a-3b)]9[2a(2a3b)+b(2a3b)]

rArr 9(2a-3b)(2a+b)9(2a3b)(2a+b)

May 19, 2017

9(2a + b)(2a - 3b) 9(2a+b)(2a3b)

Explanation:

36a^2 - 36ab - 27b^2 = 9(4a^2 - 4ab - 3b^2) 36a236ab27b2=9(4a24ab3b2)
->99 is a highest common factor for 36 and 2736and27

we try to find the product of factor for (4 * 3 = 12), then we get
12 = 6 * 2, -6 + 2 = -412=62,6+2=4
thereofore we replace -4ab to -6ab + 2ab4ab6ab+2ab

9(4a^2 - 4ab - 3b^2) = 9(4a^2 -6ab + 2ab -3b^2)9(4a24ab3b2)=9(4a26ab+2ab3b2)
We separate into 2 portions and factor it.
1. 4a^2 - 6ab = 2a(2a - 3b) 4a26ab=2a(2a3b)
2. 2ab - 3b^2 = b(2a - 3b)2ab3b2=b(2a3b)
it is correct when both of them have a same of (2a - 3b)(2a3b),
therefore,
(4a^2 -6ab + 2ab -3b^2) =2a(2a - 3b) +b(2a - 3b)= (2a + b)(2a - 3b)(4a26ab+2ab3b2)=2a(2a3b)+b(2a3b)=(2a+b)(2a3b)

therefore,
9(4a^2 -6ab + 2ab -3b^2) = 9(2a + b)(2a - 3b) 9(4a26ab+2ab3b2)=9(2a+b)(2a3b)