Chapter 1.2, Problem 23P

Simplify each expression.

${\left(\frac{s+2}{5t^2}\right)}^2$

To determine

To simplify: ${\left(\frac{s+2}{5t^2}\right)}^2$

Answer to Problem 23P

  $\frac{s^2+4s+4}{25t^4}$

Explanation of Solution

Given:

  ${\left(\frac{s+2}{5t^2}\right)}^2$

Calculation:

  $\begin{array}{l}{\left(\frac{s+2}{5t^2}\right)}^2\\ =\frac{{(s+2)}^2}{{(5t^2)}^2}\left[\because {\left(\frac{a}{b}\right)}^2=\frac{a^2}{b^2}\right]\\ $ =\frac{s^2+2(s)(2)+2^2}{5^2{(t^2)}^2}[\because {(a+b)}^2=a^2+2ab+b^2]$=\frac{s^2+4s+4}{25t^4}[\because t^2\times t^2=t^{2+2}=t^4]\end{array}$