Final answer:
To apply the distributive property to factor out the greatest common factor of 75 + 20, we identify the greatest common factor, which is 5, and then rewrite the sum as the product of the greatest common factor and the simplified sum of the terms, resulting in the expression 5 × 19 or 95.
Step-by-step explanation:
We are asked to apply the distributive property to factor out the greatest common factor from the expression 75 + 20.
First, we identify the greatest common factor for both numbers. The greatest common factor for 75 and 20 is 5 because 5 is the largest number that divides both 75 and 20 without leaving a remainder.
Applying the distributive property:
- Factor out the greatest common factor (5) from each term.
- Divide each term by the greatest common factor.
- Write the original expression as a product of the greatest common factor and the sum of the quotients from the division.
Performing the steps, we get:
5(75 ÷ 5 + 20 ÷ 5)
5(15 + 4)
5(19)
The factored form of the expression is 5 × 19, which simplifies to 95.