Question

expand the following ​

Answer 1

★Solution:-

$\bigg( \frac{2a}{5b} - \frac{5b}{2a} \bigg) {}^{ {}^{ {}^{ {}^{ 2} } } } \\ \\ \\ \implies \small{ \: \bigg( \frac{2a}{5b} \bigg) {}^{ {}^{ {}^{ {}^{2} } } } - 2a \times \frac{2a}{5b} \times \frac{5b}{2a} + \bigg(\frac{5b}{2a} \bigg) {}^{2} } \\ \\ \\ \sf \: Formula:- \\ \\ \boxed{ (a - b) {}^{2} = {a}^{2} - 2ab + {b}^{2} }\\ \\ \\ \implies \: \frac{4a {}^{2} }{25 {b}^{2} } - 2 + \frac{25 {b}^{2} }{4 {a}^{2} }$

Answer 2

Answer:

$\frac{4 {a}^{2} }{25 {b}^{2} } + \frac{25 {b}^{2} }{4 {a}^{2} } - 2$

Step-by-step explanation:

We will use a algebraic formula:

(a - b)² = a² + b² -2 x a x b

$Here, \: a = \frac{2a}{5b} ; b = \frac{5b}{2a}$

${( \frac{2a}{5b} - \frac{5b}{2a} )}^{2} = {( \frac{2a}{5b} )}^{2} + { (\frac{5b}{2a}) }^{2} - 2 \times \frac{2a}{5b} \times \frac{5b}{2a}$

$= \frac{4 {a}^{2} }{25 {b}^{2} } + \frac{25 {b}^{2} }{4 {a}^{2} } - 2$