Chapter 8.7, Problem 50PPE

a.

To determine

To solve $4x^2-100$ by removing monomial factor and apply difference of square rule.

Answer to Problem 50PPE

4(x-5)(x+5)

Explanation of Solution

Given:

  $4x^2-100$

Formula used:

  ${\text{a}}^2-b^2=(a+b)(a-b)$

Calculation:

  $\begin{array}{l}4x^2-100\\ 4(x^2-25)\\ \text{apply difference of squares rule}\\ \text{4(x-5)(x+5)}\end{array}$

b.

To determine

To solve by applying difference of squares rule and then removing monomial.

Answer to Problem 50PPE

4(x-5)(x+5)

Explanation of Solution

Given:

  $4x^2-100$

Formula used:

  ${\text{a}}^2-b^2=(a+b)(a-b)$

Calculation:

  $\begin{array}{l}4x^2-100\\ \text{apply difference of squares rule}\\ $ {(2x)}^2-{(10)}^2$(2x-10)(2x+10)\\ 2(x-5)2(x+5)\\ 4(x-5)(x+5)\end{array}$

c.

To determine

To give reason why can $4x^2-100$ be factorize in two different ways.

Explanation of Solution

  $4x^2-100$ ca be factorize in two different ways because there are two different method to solve the expression and get the answer.

d.

To determine

To solve $3x^2-75$ in two different method .is it posiible or not.

Explanation of Solution

Given:

  $3x^2-75$

Formula used:

  ${\text{a}}^2-b^2=(a+b)(a-b)$

Calculation:

  $\begin{array}{l}(a)\text{ method}\\ 3x^2-75\\ 3(x^2-25)\\ \text{apply difference of square rule}\\ \text{3(x-5)(x+5)}\\ \\ (b)\text{ method}\\ 3x^2-75\\ \text{applying difference of square rule method is not possible because }\\ \text{3 and 75 are not a perfect square}\text{.}\end{array}$