Factorise : 1+64 x^{3}

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2. Polynomials

medium

Factorise :

$1+64 x^{3}$

Option A

Option B

Option C

Option D

Solution

We have,

$1+64 x^{3}=(1)^{3}+(4 x)^{3}$

$=(1+4 x)\left\{(1)^{2}-(1)(4 x)+(4 x)^{2}\right\}$ $\left[\because a^{3}+b^{3}=(a+b)\left(a^{2}-a b+b^{2}\right)\right]$

$=(1+4 x)\left(1-4 x+16 x^{2}\right)$

$=(1+4 x)\left(16 x^{2}-4 x+1\right)$

$=(4 x+1)\left(16 x^{2}-4 x+1\right)$

Standard 9

Mathematics

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