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Factorization — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsFactorization3 Marks
Question
Solve:
$49-a^2+8 a b-16 b^2$
✓

Answer

$49-a^2+8 a b-16 b^2$
$=49-\left(a^2-8 a b+16 b^2\right)$
$=49-\left[a^2-2 \times a \times 4 b+\left(4 b^2\right)\right]$
$=7^2-\left(a-4 b^2\right)$
$=[7-(a-4 b)][7+(a-4 b)]$
$=(7-a+4 b)(7+a-4 b)$
$=-(a-4 b-7)(a-4 b+7)$
$=-(a-4 b+7)(a-4 b-7)$

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