Question

Why might you use the distributive property to simplify 3(30-2).

Answer 1

The distributive property is used to simplify 3(30-2) by multiplying both terms within the parentheses by 3 individually and then subtracting the products, resulting in the simplified answer of 96.

Step-by-step explanation:

The reason you might use the distributive property to simplify the expression 3(30-2) is that it allows you to multiply each term inside the parenthesis by 3 before subtracting the two terms. Simplifying complex expressions is a fundamental aspect of algebra, and the distributive property is a key tool for this purpose. Applying the distributive property to the given expression, we calculate 3 × 30 and 3 × (-2) separately, then subtract the second product from the first.

Let's apply the distributive property step by step:

1. 
   
2. Multiply the first term inside the parenthesis: 3 × 30 = 90.
3. 
   
4. Multiply the second term inside the parenthesis: 3 × (-2) = -6.
5. 
   
6. Subtract the second product from the first: 90 - (-6) = 90 + 6.
7. 
   
8. Combine the resulting terms: 90 + 6 = 96.

Thus, 3(30-2) simplifies to 96 using the distributive property.