Question

Factorise the following expression-
$k^4+4k^2{m}^2+4m^4$

Answer 1

$k^4+4k^2{m}^2+4m^4$

$=k^4+2k^2{m}^2+2k^2{m}^2+4m^4$

$=k^2(k^2+2m^2)+2m^2(k^2+2m^2)$

$=(k^2+2m^2)(k^2+2m^2)$

$={(k^2+2m^2)}^2$