Question

Solve the square using the binomial squares pattern.

${\left(3x^2+2\right)}^2$

Short answer

The solution is$9x^4+12x^2+4$.

Step-by-step solution

Step 1. Given information.

The given expression is${\left(3x^2+2\right)}^2$.

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

Solve it as follows:

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

Step 3. Binomial squares expression.

Hence, the binomial squares pattern are$9x^4+12x^2+4$.