Question

Find the product: $\left(5-2x\right)\left(3+x\right)$

Answer 1

Simplify using the rules of binomial products:

The given expression is $\left(5-2x\right)\left(3+x\right)$.

It can be simplified as follows,

$\left(5-2x\right)\left(3+x\right)=5\left(3+x\right)-2x\left(3+x\right)$ $\mathrm{[}\mathrm{\because }\mathrm{}\left(a+b\right)\left(c+d\right)\mathrm{=}\mathrm{a}\left(c+d\right)\mathrm{+}\mathrm{b}\left(c+d\right)\mathrm{]}$

$$\begin{gathered} \Rightarrow \left(5-2x\right)\left(3+x\right)=\left(15+5x\right)-\left(6x+2x^2\right) \\ \Rightarrow \left(5-2x\right)\left(3+x\right)=15+5x-6x-2x^2 \\ \Rightarrow \left(5-2x\right)\left(3+x\right)=15-x-2x^2 \end{gathered}$$

Hence, the product of $\left(5-2x\right)\left(3+x\right)$ is $15-x-2x^2$.