Factorize: x^4y^2- x^2y^4- x^4y^4 is x^2y^2 - Vidyadip

Question

Factorize: $x^4y^2- x^2y^4- x^4y^4$ is $x^2y^2$

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Answer

The greatest common factor of the term
$x^4 y^2-x^2 y^4$ and $x^4 y^4$ of the expression
$x^4 y^2-x^2 y^4-x^4 y^4$ is $x^2 y^2$
Also, we can write $x^4 y^2=x^2 y^4\left(x^2 y^2 \cdot x^2\right), x^2 y^4=\left(x^2 y^2 \cdot y^2\right)$ and $x^4 y^4=\left(x^2 y^2 \cdot x^2 y^2\right)$
Therefore, $x^4 y^2-x^2 y^4-x^4 y^4=\left(x^2 y^2 \cdot x^2\right)-\left(x^2 y^2 \cdot y^2\right)-\left(x^2 y^2 \cdot x^2 y^2\right)$
$=x^2 y^2\left(x^2-y^2-x^2 y^2\right)$

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