Chapter 8.4, Problem 68PFA

a.

To determine

To find: The product ${\left(2x-3\right)}^2$

Answer to Problem 68PFA

  $4x^2-12x+9$

  $C$ is the correct option.

Explanation of Solution

Given:

  ${\left(2x-3\right)}^2$

Calculation:

The given expression is

  ${\left(2x-3\right)}^2$

Apply the formula ${\left(a-b\right)}^2=a^2-2ab+b^2$

  $\begin{array}{l}{\left(2x\right)}^2-2\cdot \left(2x\right)\cdot \left(3\right)+{\left(3\right)}^2\\ =4x^2-12x+9\end{array}$

b.

To determine

To find: The product ${\left(2x+3\right)}^2$

Answer to Problem 68PFA

  $4x^2+12x+9$

  $C$ is the correct option.

Explanation of Solution

Given:

  ${\left(2x+3\right)}^2$

Calculation:

The given expression is

  ${\left(2x+3\right)}^2$

Apply the formula ${\left(a+b\right)}^2=a^2+2ab+b^2$

  $\begin{array}{l}{\left(2x\right)}^2+2\cdot \left(2x\right)\cdot \left(3\right)+{\left(3\right)}^2\\ =4x^2+12x+9\end{array}$

c.

To determine

To find: The product $\left(2x+3\right)\left(2x-3\right)$

Answer to Problem 68PFA

  $4x^2-9$

  $C$ is the correct option.

Explanation of Solution

Given:

  $\left(2x+3\right)\left(2x-3\right)$

Calculation:

The given expression is

  $\left(2x+3\right)\left(2x-3\right)$

Apply the formula $\left(a+b\right)\left(a-b\right)=a^2-b^2$

  $\begin{array}{l}{\left(2x\right)}^2-{\left(3\right)}^2\\ =4x^2-9\end{array}$