Question

Solve this question ​

Answer 1

$(5a {}^{2} - 2b {}^{2} ) {}^{2} + 40a {}^{2} b {}^{2} = (5a {}^{2} + 2b {}^{2} ) {}^{2}$

Take LHS

$25a {}^{4} - 20a {}^{2} b {}^{2} + 4b {}^{4} + 40a {}^{2} b {}^{2}$

$25a {}^{4} + 20a {}^{2} b {}^{2} + 4b {}^{4}$

$(5a {}^{2} + 2b {}^{2} ) {}^{2}$

Thanks

Answer 2

Consider 5a^2= p

and 2b^2= q

So,40a^2b^2=4(5a^2)(2b^2)=4pq

Now,LHS= (p-q)^2 + 4pq

= p^2 -2pq +q^2 +4pq

= p^2 +2pq +q^2

= (p+q)^2

= (5a^2 +2b^2)^2

= RHS