Question

factorise 216a³-2root2b³​

Answer 1

$Given \: 216a^{3} -2\sqrt{2} b^{3}$

$= 6^{3} a^{3} - (\sqrt{2})^{3} b^{3}$

$=( 6a)^{3} - (\sqrt{2}b)^{3}$

/* By algebraic identity */

$\boxed{ \pink { x^{3} - y^{3} = (x-y)(x^{2}+xy+y^{2})}}$

$= (6a-\sqrt{2}b)[ (6a)^{2} + (6a)(\sqrt{2}b) + (\sqrt{2}b)^{2} ]$

$= (6a-\sqrt{2}b)(36a^{2} + 6\sqrt{2}ab + 2b^{2} )$

Therefore.,

$\red{ 216a^{3} -2\sqrt{2} b^{3} }$

$\green {= (6a-\sqrt{2}b)(36a^{2} + 6\sqrt{2}ab + 2b^{2} ) }$

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