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Factorisation — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsFactorisation2 Marks
Question
Factorise:
$25 a^2-4 b^2+28 b c-49 c^2$
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Answer

$25 a^2-4 b^2+28 b c-49 c^2$
$=25-\left[4 b^2-28 b c+49 c^2\right]$
${\left[\because a^2-2 a b+b^2=(a-b)^2\right]}$
$=(5 a)^2-\left[(2 b)^2-2 \times 2 b \times 7 c+(7 c)^2\right]$
$=(5 a)^2-(2 b-7 c)^2$
$\left\{\because\left(a^2-b^2=(a+b)(a-b)\right\}\right.$
$=(5 a+2 b-7 c)(5 a-2 b+7 c)$

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