Chapter 12.1, Problem 7MRE

To determine

To Express: The square ${\left(\frac{1}{2}x+\frac{2}{3}\right)}^2$ as a trinomial.

Answer to Problem 7MRE

The required answer is $\frac{1}{4}{x}^2+\frac{2x}{3}+\frac{4}{9}$ .

Explanation of Solution

Given information:

  ${\left(\frac{1}{2}x+\frac{2}{3}\right)}^2$

Calculation:

  $\begin{array}{l}{\left(\frac{1}{2}x+\frac{2}{3}\right)}^2\\ ={\left(\frac{1}{2}x\right)}^2+2\cdot \frac{1}{2}x\cdot \frac{2}{3}+{\left(\frac{2}{3}\right)}^2\end{array}$

(Using ${\left(a+b\right)}^2=a^2+2ab+b^2$ )

  $=\frac{1}{4}{x}^2+\frac{2x}{3}+\frac{4}{9}$

(Simplify)

So, the required trinomial is $\frac{1}{4}{x}^2+\frac{2x}{3}+\frac{4}{9}$ .