Question

14. Simplify :
(i)(a/2b+2b/a)²-(2b/a-a/2b)²​

Answer 1

Step-by-step explanation:

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

$= ( { \frac{ {a}^{2} + 4 {b}^{2} }{2ab})}^{2} - {( \frac{4 {b}^{2} - {a}^{2} }{2ab} )}^{2}$

$= \frac{{ ({a}^{2} + 4 {b}^{2}) }^{2}}{ {(2ab)}^{2} } - \frac{ {(4 {b}^{2} - {a}^{2} )}^{2} }{ {(2ab)}^{2} }$

$= \frac{{a}^{4} + 16 {b}^{4} + 8 {a}^{2} {b}^{2} }{4 {a}^{2} {b}^{2} } - \frac{16{b}^{4} + {a}^{4} - 8 {a}^{2} {b}^{2} }{4 {a}^{2} {b}^{2} }$

$= \frac{{a}^{4} + 16 {b}^{4} + 8 {a}^{2} {b}^{2} - {a}^{4} - 16 {b}^{4} + 8 {a}^{2} {b}^{2} }{4 {a}^{2} {b}^{2} }$

$= \frac{8 {a}^{2} {b}^{2} + 8 {a}^{2} {b}^{2} }{4 {a}^{2} {b}^{2} }$

$= \frac{16 {a}^{2} {b}^{2}}{4 {a}^{2} {b}^{2} }$

$= 4$

Answer 2

Step-by-step explanation:

The above answer will surely help You....