Chapter 8, Problem 41SGR

To determine

To use distributive property to factor the given polynomial.

Answer to Problem 41SGR

  $(a+b)(a-4c)$

Explanation of Solution

Given:

Polynomial: $a^2-4ac+ab-4bc$

Concept used:

Distributive property: $a(b+c)=a\cdot b+a\cdot c$

Calculation:

Consider the polynomial $a^2-4ac+ab-4bc$ ,

Grouping the similar terms,

  $\begin{array}{l}\Rightarrow a^2-4ac+ab-4bc\\ \Rightarrow (a^2-4ac)+(ab-4bc)\end{array}$

Applying the distributive property,

Finding out the common terms in each term of the expression,

Here, $(a-4c)$ is common term.

  $\begin{array}{l}\Rightarrow (a^2-4ac)+(ab-4bc)\\ \Rightarrow a(a-4c)+b(a-4c)\end{array}$

  $\Rightarrow (a+b)(a-4c)$

Conclusion:

Therefore, the factors of the given polynomial are $(a+b)(a-4c).$