Factorize: 10 m^3 n^2+15 m^4 n-20 m^2 n^3 - Vidyadip

Question

Factorize:
$10 m^3 n^2+15 m^4 n-20 m^2 n^3$

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Answer

The greatest common factor of the terms
$10 m^3 n^2, 15 m^4 n$ and $-20 m^2 n^3$ of the expression $10 m^3 n^2+15 m^4 n-20 m^2 n^3$ is $5 m^2 n$
Now,
$10 m^3 n^2=5 m^2 n \cdot 2 m n \\
15 m^4 n=5 m^2 n \cdot 3 m^2 \\
-20 m^2 n^3=5 m^2 n \cdot-4 n^2$
Hence, $10 m^3 n^2+15 m^2 n-20 m^2 n^3$ can be factorised as $5 m^2 n\left(2 m n+3 m^2-4 n^2\right)$.

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