Chapter 8.4, Problem 1P

a.

To determine

To find:The simpler form of the product ${(n-7)}^2$

Answer to Problem 1P

  $n^2-14n+49$

Explanation of Solution

Given information:The expression ${(n-7)}^2$

Calculation:

  $\begin{array}{l}$ {(n-7)}^2$$ =n^2-2\cdot n\cdot 7+7^2[\because {(a-b)}^2=a^2-2ab+b^2]$=n^2-14n+49\end{array}$

Thus, ${(n-7)}^2=n^2-14n+49$

b.

To determine

To find:The simpler form of the product ${(2x+9)}^2$

Answer to Problem 1P

  $4x^2+36x+81$

Explanation of Solution

Given information:The expression ${(2x+9)}^2$

Calculation:

  $\begin{array}{l}$ {(2x+9)}^2$$ ={(2x)}^2+2\cdot 2x\cdot 9+9^2[\because {(a+b)}^2=a^2+2ab+b^2]$=4x^2+36x+81\end{array}$

Thus, ${(2x+9)}^2=4x^2+36x+81$