Question

Factors of a^3-2root2b^3 are

Answer 1

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

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

/* By algebraic identity */

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

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

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

Therefore.,

$\red{Factors \:of \: a^{3} - 2\sqrt{2} b^{3} }$

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

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Answer 2

ANSWER ✔

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

✯IDENTITY IN USE,

$\large{\boxed{\bf{ \star\:\: x^3-y^3= (x-y)(x^2+y^2+xy)\:\: \star}}}$

$\large\underline\bold{SOLUTION,}$

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

$\implies (a-\sqrt{2}b)( a^{2} + a \times \sqrt{2}b+ (\sqrt{2}b)^{2} )$

$\implies (a-\sqrt{2}b)(a^{2} + \sqrt{2}ab+ 2b^{2})$

$\large{\boxed{\bf{ \star\:\: (a-\sqrt{2}b)(a^{2} + \sqrt{2}ab+ 2b^{2})\:\: \star}}}$

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