Factorise 216a³-2root2b³

1.	Factorise 216a³-2root2b³
Answer» align="absmiddle" alt="Given \: 216a^{3} -2\sqrt{2} b^{3}" class="latex-formula" ID="TexFormula1" SRC="https://tex.z-dn.net/?f=%20Given%20%5C%3A%20216a%5E%7B3%7D%20-2%5Csqrt%7B2%7D%20b%5E%7B3%7D%20" TITLE="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., $\red{ 216a^{3} -2\sqrt{2} b^{3} }$ $\green {= (6a-\sqrt{2}b)(36a^{2} + 6\sqrt{2}ab + 2b^{2} ) }$ ••♪

Answer»

align="absmiddle" alt="Given \: 216a^{3} -2\sqrt{2} b^{3}" class="latex-formula" ID="TexFormula1" SRC="https://tex.z-dn.net/?f=%20Given%20%5C%3A%20216a%5E%7B3%7D%20-2%5Csqrt%7B2%7D%20b%5E%7B3%7D%20" TITLE="Given \: 216a^{3} -2\sqrt{2} b^{3}">

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