Question

factorise 24a^3+81b^3

Answer 1

$<b >Hey here is your answer$

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$= 24 {a}^{3} + 81 {b}^{3} \\ \\ = 3(8 {a}^{3} + 27 {b}^{3} ) \\ \\ =3[(2a {)}^{3} + (3b {)}^{3} ]$

using identity :-

$= {a}^{3} + {b}^{3} = (a + b)( {a}^{2} + {b}^{2} - ab) \\ \\ = 3(2a - 3b)[ {(2a)}^{2} + {(3b)}^{2} - 2a \times 3b)] \\ \\ = 3(2a - 3b)[ {4a}^{2} + {9b}^{2} - 6ab)]$


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hope this helps you

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