Q.221. - Intermediate Algebra

Question

Solve the square using the binomial squares pattern.

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

Step-by-Step Solution

Answer

The solution is $x^2+\frac{4x}{3}+\frac{4}{9}$.

Step 1. Given information.

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

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:

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

Step 3. Binomial squares expression.

Hence, the binomial squares pattern are $x^2+\frac{4x}{3}+\frac{4}{9}$.