Factorise: a^{3} - 2sqrt{2}b^{3} | vedclass

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Question

(A) We use the algebraic identity: $a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2})$.Given expression: $a^{3} - 2\sqrt{2}b^{3}$.Rewrite the expression as:

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) We use the algebraic identity: $a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2})$.Given expression: $a^{3} - 2\sqrt{2}b^{3}$.Rewrite the expression as: $a^{3} - (\sqrt{2}b)^{3}$.Applying the identity where $x = a$ and $y = \sqrt{2}b$:$= (a - \sqrt{2}b)((a)^{2} + (a)(\sqrt{2}b) + (\sqrt{2}b)^{2})$.$= (a - \sqrt{2}b)(a^{2} + \sqrt{2}ab + 2b^{2})$.

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

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