Factorize: 2 a^4 b^4-3 a^3 b^5+4 a^2 b^5 - Vidyadip

Question

Factorize:
$2 a^4 b^4-3 a^3 b^5+4 a^2 b^5$

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Answer

The greatest common factor of the terms
$2 a^4 b^4,-3 a^3 b^5$ and $4 a^2 b^5$ of the expression $2 a^4 b^4-3 a^3 b^5+4 a^2 b^5$ is $a^2 b^4$
Now,
$2 a^4 b^4=a^2 b^4 \cdot 2 a^2$
$-3 a^3 b^5=a^2 b^4 \cdot-3 a b$
$4 a^2 b^5=a^2 b^4 \cdot 4 b$
Hence, $\left(2 a^4 b^4-3 a^3 b^5+4 a^2 b^5\right)$ can be factorised as $\left[a^2 b^4\left(2 a^2-3 a b+4 b\right)\right]$.

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