Math Problem Statement

Which expression is equivalent to 4(3n - 5)?

Solution

The problem asks to find which expression is equivalent to 4(3n5)4(3n - 5).

To solve this, we need to distribute the 4 across the terms inside the parentheses:

4(3n5)=43n454(3n - 5) = 4 \cdot 3n - 4 \cdot 5

Simplifying:

4(3n5)=12n204(3n - 5) = 12n - 20

So, the correct expression is 12n2012n - 20, which matches the second option.

Would you like more details on this, or do you have any questions?

Here are five related questions to expand on this:

  1. How would the expression change if it were 5(3n4)5(3n - 4)?
  2. What is the general rule for distributing a number across a binomial?
  3. How would you factor the expression 12n2012n - 20?
  4. What happens when the binomial is 3n+53n + 5 instead of 3n53n - 5?
  5. How do you handle distribution with variables and constants?

Tip: Always remember to apply the distributive property to each term inside the parentheses, including both variables and constants!

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Math Problem Analysis

Mathematical Concepts

Algebra
Distributive Property

Formulas

Distributive Property: a(b + c) = ab + ac

Theorems

Distributive Property

Suitable Grade Level

Grades 6-8