Question

Solve the square using the binomial squares pattern.

${\left(2y-3z\right)}^2$

Short answer

The solution is$4y^2-12yz+9z^2$.

Step-by-step solution

Step 1. Given information.

The given expression is${\left(2y-3z\right)}^2$.

Step 2. Simplify the given expression by using the binomial squares pattern a-b2=a2-2ab+b2.

Solve it as follows:

$$\begin{gathered} {\left(2y-3z\right)}^2={\left(2y\right)}^2-2\times 2y\times 3z+{\left(3z\right)}^2 \\ \Rightarrow 4y^2-12yz+9z^2 \end{gathered}$$

Step 3. Binomial squares expression.

Hence, the binomial squares pattern are$4y^2-12yz+9z^2$.