Chapter 12.7, Problem 48STP

To determine

To calculate ${(h-2)}^2$

Answer to Problem 48STP

  $b^2-18b+81$

Explanation of Solution

Given:

Equation: $h+4=b-3$

Calculation:

Consider $h+4=b-3,$

Calculate h following the steps below:

Subtract 4 on both sides of the equation.

  $\begin{array}{c}h+4-4=b-3-4\\ h=b-7\end{array}$

Now, finding the value of ${(h-2)}^2$ ,

Substitute h in the above expression.

  $\begin{array}{}$ {(h-2)}^2={((b-7)-2)}^2$$ ={(b-9)}^2$\end{array}$

Using the algebraic identity ${(a-b)}^2=a^2-2ab+b^2,$

  $\begin{array}{c}$ {(h-2)}^2={(b-9)}^2$$ =b^2-2(b)(9)+9^2$=b^2-18b+81\end{array}$

Conclusion:

Therefore, ${(h-2)}^2=b^2-18b+81.$