Question

(4/5p+5/3q)² expand the expression by using suitable identity​

Answer 1

See the attach image
Your ans in this pic

Answer 2

Identity used :

$\large \boxed{ \boxed{ \sf {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} }}$

Calculation :

$\implies\sf {\bigg( \frac{4}{5}p + \frac{5}{3}q\bigg)}^{2} \\ \\ \implies\sf { \bigg( \frac{4}{5}q\bigg) }^{2} + 2 \times \frac{4}{5}p \times \frac{5}{3}q + {\bigg( \frac{5}{3}q\bigg) }^{2} \\ \\\implies\sf \frac{16}{25} {q}^{2} + \frac{8}{3}pq + \frac{25}{9} {q}^{2}$

Other important identities :

$\large\implies \sf {(a - b)}^{2} = {a}^{2}- 2ab + {b}^{2} \\ \\\large\implies \sf a^2 - b^2 = (a+b)(a-b) \\ \\\large\implies \sf (x+a)(x+b) = x^2 + (a+b)x+ab \\ \\ \large\implies \sf a^3 - b^3 = (a-b)(a^2 + ab + b^2)\\ \\ \large\implies \sf {(a+b)}^{2} - {(a-b)}^{2} =4ab$