Question
Factorise : $4a^2- 12a + 9 - 49b^2$
✓
Answer
$4a^2 - 12a + 9 - 49b^2= (2a)^2 - 12a + (3)^2 - 49b^2$
$= (2a)^2 - 2(2a)(3) + (3)^2 - (7b)^2 ...[\because (a - b)^2= a^2-2ab + b^2]$
$= (2a - 3)^2 - (7b)^2$
$= (2a - 3 - 7b)(2a - 3 + 7b) ...[\because a^2 - b^2 = (a + b)(a - b)]$
$= (2a)^2 - 2(2a)(3) + (3)^2 - (7b)^2 ...[\because (a - b)^2= a^2-2ab + b^2]$
$= (2a - 3)^2 - (7b)^2$
$= (2a - 3 - 7b)(2a - 3 + 7b) ...[\because a^2 - b^2 = (a + b)(a - b)]$
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