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Factorization — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsFactorization3 Marks
Question
Solve:
$a^2-8 a b+16 b^2-25 c^2$
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Answer

$a^2-8 a b+16 b^2-25 c^2$
$=\left(a^2-8 a b+16 b\right)-25 c^2$
$=\left[a^2-2 \times a \times 4 b+(4 b)^2\right]-25 c^2$
$=(a-4 b)^2-(5 c)^2$
$=\left[(a-b)^2-5 c\right]\left[(a-4 b)^2+5 c\right]$
$=(a-4 b-5 c)(a-4 b+5 c)$

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