Question

Find the product of the below expression.

$\left(2x+y\right)\left(x-2y\right)$

Short answer

The solution is$2x^2-3xy-2y^2$.

Step-by-step solution

Step 1. Given information.

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

Step 2. Simplify the expressions by using the distributive property ab±c=ab±ac.

Solve it as follows:

$$\begin{gathered} \left(2x+y\right)\left(x-2y\right)=2x\left(x-2y\right)+y\left(x-2y\right) \\ \Rightarrow 2x^2-4xy+xy-2y^2 \\ \Rightarrow 2x^2-3xy-2y^2 \end{gathered}$$

Step 3. Simplified expression.

Hence, the required expression is$2x^2-3xy-2y^2$.