Q.224. - Intermediate Algebra

Question

Solve the square using the binomial squares pattern.

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

Step-by-Step Solution

Answer

The solution is $9x^4+12x^2+4$.

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

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 $9x^4+12x^2+4$.