Question

Factorize a^3-3 root 3 b^3​

Answer 1

Step-by-step explanation:

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

$\bold {\underline{ \red{formula \: used}}} \longrightarrow \\ 1) \: {x}^{3} - {y}^{3} = (x - y) \: ( {x}^{2} + {y}^{2} + xy)$