Factorize 9(x + y)2 – 4(x – y)2
-
A.
(x + y)(5x + y) -
B.
(x + y)2 -
C.
(x + 5y)(5x + y) -
D.
5(x + y)2
Correct Answer: Option C
Explanation
9(x + y)2 – 4(x – y)2
Using difference of two squares which says
a2 – b2 = (a + b)(a – b) = 9(x + y)2 – 4(x – y)2
= [3(x + y)]2 – [2(x – y)]-2
= [3(x + y) + 2(x – y) + 2(x – y)][3(x + y) – 2(x – y)]
= [3x +3y + 2x – 2y][3x + 3y – 2x + 2y]
= (5x + y)(x + 5y)