Chapter 8.4, Problem 4P

a.

To determine

To find: The simpler form of the product $(x+9)(x-9)$.

Answer to Problem 4P

  $x^2-81$

Explanation of Solution

Given information: The expression $(x+9)(x-9)$

Calculation:

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

Thus, the simpler form is $x^2-81$ .

b.

To determine

To find: The simpler form of the product $(6+m^2)(6-m^2)$.

Answer to Problem 4P

  $36-m^4$

Explanation of Solution

Given information: The expression $(6+m^2)(6-m^2)$

Calculation:

  $\begin{array}{l}(6+m^2)(6-m^2)\\ $ ={(6)}^2-{(m^2)}^2[\because a^2-b^2=(a+b)(a-b)]$=36-m^4\end{array}$

Thus, the simpler form is $36-m^4$ .

c.

To determine

To find: The simpler form of the product $(3c-4)(3c+4)$.

Answer to Problem 4P

  $9c^2-16$

Explanation of Solution

Given information: The expression $(3c-4)(3c+4)$

Calculation:

  $\begin{array}{l}(3c-4)(3c+4)\\ =(3c+4)(3c-4)\\ $ ={(3c)}^2-{(4)}^2[\because a^2-b^2=(a+b)(a-b)]$=9c^2-16\end{array}$

Thus, the simpler form is $9c^2-16$ .