36a^2 - 36ab - 27b^2 = 9(4a^2 - 4ab - 3b^2) 36a2−36ab−27b2=9(4a2−4ab−3b2)
->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=6⋅2,−6+2=−4
thereofore we replace -4ab to -6ab + 2ab−4ab→−6ab+2ab
9(4a^2 - 4ab - 3b^2) = 9(4a^2 -6ab + 2ab -3b^2)9(4a2−4ab−3b2)=9(4a2−6ab+2ab−3b2)
We separate into 2 portions and factor it.
1. 4a^2 - 6ab = 2a(2a - 3b) 4a2−6ab=2a(2a−3b)
2. 2ab - 3b^2 = b(2a - 3b)2ab−3b2=b(2a−3b)
it is correct when both of them have a same of (2a - 3b)(2a−3b),
therefore,
(4a^2 -6ab + 2ab -3b^2) =2a(2a - 3b) +b(2a - 3b)= (2a + b)(2a - 3b)(4a2−6ab+2ab−3b2)=2a(2a−3b)+b(2a−3b)=(2a+b)(2a−3b)
therefore,
9(4a^2 -6ab + 2ab -3b^2) = 9(2a + b)(2a - 3b) 9(4a2−6ab+2ab−3b2)=9(2a+b)(2a−3b)