Question:
Factorize each of the following expression:
49(a − b)2 − 25(a + b)2
Solution:
$49(a-b)^{2}-25(a+b)^{2}$
$=[7(a-b)]^{2}-[5(a+b)]^{2}$
$=[7(a-b)-5(a+b)][7(a-b)+5(a+b)]$
$=(7 a-7 b-5 a-5 b)(7 a-7 b+5 a+5 b)$
$=(2 a-12 b)(12 a-2 b)$
$=2(a-6 b) 2(6 a-b)$
$=4(a-6 b)(6 a-b)$
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