1.

Factorize (x - y)2 – 7(x2 – y2) + 12(x + y)21. 2(3x + 5y) (x + 2y)2. 3(2x + 5y) (2x + y)3. 5(3x + 2y) (x + 2y)4. 3(5x + 2y) (2x + y)

Answer» Correct Answer - Option 1 : 2(3x + 5y) (x + 2y)

(x - y)2 - 7(x2 - y2) + 12(x + y)2

= (x - y)2 – 7(x – y) (x + y) + 12(x + y)2 [As x2 – y2 = (x +y) (x + y)]

Let (x – y) = p & (x + y) = q, then

(x - y)2 - 7(x2 - y2) + 12(x + y)2

= p2 - 7pq + 12q2

= p2 - 4pq - 3pq + 12q2

= p(p - 4q) - 3q(p - 4q)

= (p - 3q) (p - 4q)

= [(x - y) - 3(x + y)] [(x - y) - 4(x + y)] [As (x - y) = p and (x + y) = q]

= (- 2x - 4y) (- 3x - 5y)

= 2(3x + 5y) (x + 2y)


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