Chapter 8, Problem 44SGR

To determine

To factorize the given expression.

Answer to Problem 44SGR

  $(6a-5)(4b+9)$

Explanation of Solution

Given:

Expression: $24ab+54a-20b-45$

Concept used:

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

Calculation:

Consider the expression $24ab+54a-20b-45$ ,

  $\begin{array}{l}\Rightarrow 24ab+54a-20b-45\\ \Rightarrow (24ab+54a)+(-20b-45)\end{array}$

Applying the distributive property,

  $\begin{array}{l}\Rightarrow 6a(4b+9)-5(4b+9)\\ \Rightarrow (6a-5)(4b+9)\end{array}$

Conclusion:

Therefore, the factors of the given expression are $(6a-5)(4b+9).$