Q.219. - Intermediate Algebra

Question

Solve the square using the binomial squares pattern.

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

Step-by-Step Solution

Answer

The solution is $4y^2-12yz+9z^2$.

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 - b 2 = a 2 - 2 a b + b 2 .

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 $4y^2-12yz+9z^2$.