Chapter 1.4, Problem 49PPS

To determine

To simplify the expression:

  $\left(\frac{1}{3}-2b\right)27$

Using the distributive property.

Answer to Problem 49PPS

  $\left(\frac{1}{3}-2b\right)27=9-54b$

Explanation of Solution

Given:

  $6\left(2c-c{d}^2+d\right)$

Concept Used:

Distributive property:

  $a\left(b\pm c\pm d\right)=ab\pm ac\pm ad$

Calculation:

In order to simplify the expression $\left(\frac{1}{3}-2b\right)27$

Use the distributive property which is:

  $a\left(b\pm c\pm d\right)=ab\pm ac\pm ad$

As,

  $\begin{array}{c}\left(\frac{1}{3}-2b\right)27=27\left(\frac{1}{3}-2b\right),\text{ commutative property}\\ \text{=27}\times \frac{1}{3}-27\times 2b\\ =9-54b\end{array}$

Thus, simplified form of given expression is:

  $\left(\frac{1}{3}-2b\right)27=9-54b$