Question

Factorize:
5x² + 33xy − 14y²

Answer 1

We have:
$5x^2+33xy-14y^2$
We have to split 33 into two numbers such that their sum is 33 and their product is ($-$70), i.e., $5\times \left(-14\right)$.
Clearly, $35+\left(-2\right)=33\mathrm{and}35\times \left(-2\right)=-70$.

$$\begin{gathered} \therefore 5x^2+33xy-14y^2=5x^2+35xy-2xy-14y^2 \\ =5x(x+7y)-2y(x+7y) \\ =(x+7y)(5x-2y) \end{gathered}$$