Question

expand [2a/5b - 5b/2a ] ^2​

Answer 1

Answer:

( 2a/5b + 5b/2a ) ( 2a/ 5b - 5b/2a )

Answer 2

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

Step-by-step explanation:

Question:  Expand $[\frac{2a}{5b} - \frac{5b}{2a} ] ^{2}$

Solution:  

⇒ $[\frac{2a}{5b} - \frac{5b}{2a} ] ^{2}$

Using the identity, (a - b)² = a² - 2ab + b²

We get,

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

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

Hence, the required answer is   $\frac{4a^{2} }{25b^{2} } + \frac{25b^{2} }{4a^{2} } - 2$

Thanks!