Chapter 4.1, Problem 29PPS

To determine

To evaluate: $\left(x-3\right)\left(-7\right)$ using distributive property

Answer to Problem 29PPS

  $-7x+21$

Explanation of Solution

Given information:

  $\left(x-3\right)\left(-7\right)$

Concept Used:

Distributive Property: The product sum or difference of two or more numbers inside a parentheses with another number outside the parentheses is equivalent to the sum or difference of product of number outside the parentheses with each number inside the parenthesis. i.e.-

  $a\left(b+c-d\right)=ab+ac-ad$

Calculation:

  $\left(x-3\right)\left(-7\right)=\left(x+\left(-3\right)\right)\left(-7\right)\mathrm{...}\left[a-b=a+\left(-b\right)\right]$

We can write the given expression in distributive form as-

  $\left(x+\left(-3\right)\right)\left(-7\right)=\left(x\right)\left(-7\right)+\left(-3\right)\left(-7\right)$

This can further be simplified as-

  $\left(x\right)\left(-7\right)+\left(-3\right)\left(-7\right)=-7x+21$