Home » Factorize 9(x + y)2 – 4(x – y)2

Factorize 9(x + y)2 – 4(x – y)2

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)

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