Factorise : a^{3}-2 √{2} b^{3}

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2. Polynomials

easy

Factorise :

$a^{3}-2 \sqrt{2} b^{3}$

Option A

Option B

Option C

Option D

Solution

$a^{3}-2 \sqrt{2 b^{3}}=(a)^{3}-(\sqrt{2} b)^{3}$

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

$=(a-\sqrt{2} b)\left(a^{2}+\sqrt{2} a b+2 b^{2}\right)$

Standard 9

Mathematics

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