Question

Factorize the following:
x⁴y² − x²y⁴ − x⁴y⁴

Answer 1

\[\text{ The greatest common factor of the terms }x^4 y^2 , x^2 y^4 and x^4 y^4\text{ of the expression }x^4 y^2 - x^2 y^4 - x^4 y^4\text{ is }x^2 y^2 . \]
\[\text{ Also, we can write }x^4 y^2 = x^2 y^2 \times x^2 , x^2 y^4 = x^2 y^2 \times y^2\text{ and }x^4 y^4 = x^2 y^2 \times x^2 y^2 . \]
\[ \therefore x^4 y^2 - x^2 y^4 - x^4 y^4 = x^2 y^2 \times x^2 - x^2 y^2 \times y^2 - x^2 y^2 \times x^2 y^2 \]
\[ = x^2 y^2 ( x^2 - y^2 - x^2 y^2 )\]