Theory:

Factorisation by taking out the common factor from each term
1. Consider the expression $3{x}^{3}-15{x}^{2}+12x$.

In all the term, $3x$ is taken commonly outside.

$\left(3x×{x}^{2}\right)+\left(3x×-5x\right)+\left(3x×4\right)$

$=3x\left({x}^{2}-5x+4\right)$

2.  Consider the expression $10\mathit{xy}+5{x}^{3}y$.

Here the term $5\mathit{xy}$ is common in the expression.

$10\mathit{xy}+5{x}^{3}y$

$\begin{array}{l}=\left(5\mathit{xy}×2+5\mathit{xy}×{x}^{2}\right)\\ \\ =5\mathit{xy}\left(2+{x}^{2}\right)\end{array}$