Question

Expand:-
$({1+\frac{2}{3} a}^{3})$
​

Answer 1

Question :-

To Expand ---

$(1 + \frac{2}{3}) {}^{3}$

Solution :-

● Using identity --

(a + b) ^3 = a^3 + b^3 + 3a^2b + 3ab^2

$({1+\frac{2}{3} a}^{3}) \\ ({1+\frac{2}{3} a}^{3}) = \\ (1) {}^{3} + (\frac{2}{3}) {}^{3} + 3(1) {}^{2} ( \frac{2}{3}) + 3(1)( \frac{2}{3 }) {}^{2} \\ 1 + \frac{8}{27} + 2 + \frac{4}{3}$

● The final answer will become --

⟹ 3 + (8 + 36)/27

⟹ 3/1 + 44/27

⟹ (81 + 44) / 27

⟹ 125/ 27

Hope it helps !