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Factorisation of Polynomials — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsFactorisation of Polynomials2 Marks
Question
Factorise:
$(2 a+1)^3+(a-1)^3$
✓

Answer

$(2 a+1)^3+(a-1)^3$
$=(2 a+1+a-1)\left[(2 a+1)^2-(2 a+1)(a-1)+(a-1)^2\right]$
$=(3 a)\left[4 a^2+4 a+1-2 a^2+2 a-a+1+a^2-2 a+1\right]$
$=3 a\left(3 a^2+3 a+3\right)$
$=9 a\left(a^2+a+1\right)$

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