Question

Simplify: ${(m^2+2n^2)}^2-4m^2{n}^2$

Answer 1

Using $(x+y{)}^2=x^2+y^2+2xy$.

Given:${(m^2+2n^2)}^2-4m^2{n}^2$ we apply the above identity as follows:

${(m^2+2n^2)}^2-4m^2{n}^2={\left(m^2\right)}^2+{\left(2n^2\right)}^2+(2\times m^2\times 2n^2)-4m^2{n}^2=m^4+4n^4+4m^2{n}^2-4m^2{n}^2=m^4+4n^4$

Hence, ${(m^2+2n^2)}^2-4m^2{n}^2=m^4+4n^4$.