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Factorization Of Algebraic Expressions — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions2 Marks
Question
Factorize the following expressions: $2\sqrt{2}\text{a}^3+3\sqrt{3}\text{b}^3+\text{c}^3-3\sqrt{6}\text{abc}$
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Answer

$2\sqrt{2}\text{a}^3+3\sqrt{3}\text{b}^3+\text{c}^3-3\sqrt{6}\text{abc}$$=\big(\sqrt{2}\text{a}\big)^3+\big(\sqrt{3}\text{b}\big)^3+\text{c}^3-3\times\sqrt{2}\text{a}\times\sqrt{3}\text{b}\times\text{c}$
$=\big(\sqrt{2}\text{a}+\sqrt{3}\text{b}+\text{c}\big)\Big(\big(\sqrt{2}\text{a}\big)^2+\big(\sqrt{3}\text{b}\big)^2+\\\text{c}^2-(\sqrt{2}\text{a}\big)(\sqrt{3}\text{b}\big)-(\sqrt{3}\text{b}\big)\text{c}-(\sqrt{2}\text{a}\big)\text{c}\Big)$
$=\big(\sqrt{2}\text{a}+\sqrt{3}\text{b}+\text{c}\big)\big(2\text{a}^2+3\text{b}^2+\text{c}^2-\sqrt{6}\text{ab}-\sqrt{3}\text{bc}-\sqrt{2}\text{ac}\big)$
$\therefore2\sqrt{2}\text{a}^3+3\sqrt{3}\text{b}^3+\text{c}^3-3\sqrt{6}\text{abc}$
$=\big(\sqrt{2}\text{a}+\sqrt{3}\text{b}+\text{c}\big)\big(2\text{a}^2+3\text{b}^2+\text{c}^2-\sqrt{6}\text{ab}-\sqrt{3}\text{bc}-\sqrt{2}\text{ac}\big)$

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