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Factorisation of Polynomials — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsFactorisation of Polynomials2 Marks
Question
Factorise:
$216+27 b^3+8 c^3-108 b c$
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Answer

$216+27 b^3+8 c^3-108 b c$
$=(6)^3+(3 b)^3+(2 c)^3-3 \times 6 \times 3 b \times 2 c$
$=(6+3 b+2 c)\left[6^2+(3 b)^2+(2 c)^2-6 \times 3 b-3 b \times 2 c-2 c \times 6\right]$
$=(6+3 b+2 c)\left(36+9 b^2+4 c^2-18 b-6 b c-12 c\right)$

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