Question

Factorize the following:
x⁴y² − x²y⁴ − x⁴y⁴

Answer 1

$$\begin{gathered} Thegreatestcommonfactoroftheterms{x}^4{y}^2,x^2{y}^{4}and{x}^4{y}^{4}oftheexpression{x}^4{y}^2-x^2{y}^4-x^4{y}^{4}is{x}^2{y}^2. \\ Also,wecanwrite{x}^4{y}^2=x^2{y}^2\times x^2,x^2{y}^4=x^2{y}^2\times y^{2}and{x}^4{y}^4=x^2{y}^2\times x^2{y}^2. \\ \therefore x^4{y}^2-x^2{y}^4-x^4{y}^4=x^2{y}^2\times x^2-x^2{y}^2\times y^2-x^2{y}^2\times x^2{y}^2 \\ =x^2{y}^2(x^2-y^2-x^2{y}^2) \end{gathered}$$