Chapter 4.1, Problem 28PPS

To determine

To evaluate: $-5\left(f-5\right)$ using distributive property

Answer to Problem 28PPS

  $-5f+25$

Explanation of Solution

Given information:

  $-5\left(f-5\right)$

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:

  $-5\left(f-5\right)=-5\left(f+\left(-5\right)\right)\mathrm{...}\left[a-b=a+\left(-b\right)\right]$

We can write the given expression in distributive form as-

  $-5\left(f+\left(-5\right)\right)=-5\left(f\right)+\left(-5\right)\left(-5\right)$

This can further be simplified as-

  $-5\left(f\right)+\left(-5\right)\left(-5\right)=-5f+25$