Question

select a suitable identity and find the following products
$(a{x}^2+b{y}^2)(a{x}^2+b{y}^2)$

Answer 1

$(a{x}^2+b{y}^2)(a{x}^2+b{y}^2)={(a{x}^2+b{y}^2)}^2$

$={\left(a{x}^2\right)}^2+{\left(b{y}^2\right)}^2+2\left(a{x}^2\right)\left(b{y}^2\right)[\text{Using identity:}{(a+b)}^2=a^2+b^2+2ab]$

$=a^2{x}^4+b^2{y}^4+2ab{x}^2{y}^2$