Question
Find the following product:
$\text{a}^3 - 2\sqrt{2}\text{b}^3$
$\text{a}^3 - 2\sqrt{2}\text{b}^3$
✓
Answer
$\text{a}^3 - 2\sqrt{2}\text{b}^3=(\text{a})^3 - (\sqrt{2}\text{b})^3$
$(\text{a} - \sqrt{2}\text{b})\big\{(\text{a})^2 +(\text{a}) (\sqrt{2}\text{b})+(\sqrt{2}\text{b})^2\big\}$
$\left[\therefore a^3-b^3=(a-b)\left(a^2+a b+b^2\right)\right]$
$(\text{a} - \sqrt{2}\text{b})(\text{a}^2 + \sqrt{2}\text{ab}+2\text{b}^2)$
$(\text{a} - \sqrt{2}\text{b})\big\{(\text{a})^2 +(\text{a}) (\sqrt{2}\text{b})+(\sqrt{2}\text{b})^2\big\}$
$\left[\therefore a^3-b^3=(a-b)\left(a^2+a b+b^2\right)\right]$
$(\text{a} - \sqrt{2}\text{b})(\text{a}^2 + \sqrt{2}\text{ab}+2\text{b}^2)$
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