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Factorise 216a³-2root2b³amd please don't write "I don't know"If you know then only answerplease ​

Answer»

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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