Question

Solve by using suitable identity: $a^4-b^4+{2b}^2-1$

Answer 1

$a^4-b^4+2b^2-1$

$\Rightarrow$$a^4-(b^4-2b^2+1)$

$\Rightarrow$$a^4-({\left(b^2\right)}^2-2b^2+1)$

$\Rightarrow$$a^4-{(b^2-1)}^2={\left(a^2\right)}^2-{(b^2-1)}^2$

$=(a^2+b^2-1)(a^2-b^2+1)$