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Polynomials — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsPolynomials2 Marks
Question
Factorise:
$1+64 x^3$
✓

Answer

We have,
$1+64 x^3=(1)^3+(4 x)^3$
$=(1+4 x)\left\{(1)^2-(1)(4 x)+(4 x)^2\right\}$
${\left[\therefore a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right]}$
$=(1+4 x)\left(1-4 x+16 x^2\right)$
$=(1+4 x)\left(16 x^2-4 x+1\right)$
$=(4 x+1)\left(16 x^2-4 x+1\right)$

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