Chapter 8, Problem 43SGR

To determine

To use distributive property to factor the given polynomial.

Answer to Problem 43SGR

  $(3a+5b)(-3n+8m)$

Explanation of Solution

Given:

Polynomial: $24am-9an+40bm-15bn$

Concept used:

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

Calculation:

Consider the polynomial $24am-9an+40bm-15bn$ ,

Group the similar terms,

  $\begin{array}{l}\Rightarrow 24am-9an+40bm-15bn\\ \Rightarrow (-9an-15bn)+(24am+40bm)\end{array}$

Applying the distributive property,

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

Here, $(3a+5b)$ is common term.

  $\begin{array}{l}\Rightarrow (-9an-15bn)+(24am+40bm)\\ \Rightarrow -3n(3a+5b)+8m(3a+5b)\\ \Rightarrow (3a+5b)(-3n+8m)\end{array}$

Conclusion:

Therefore, the factors of the given polynomial are $(3a+5b)(-3n+8m).$