Distributive Property Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Distributive Property.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Multiplication distributes over addition: a(b + c) = ab + ac, linking two operations together.

Three packs of (2 red + 4 blue) = (3 \times 2 red) + (3 \times 4 blue) = 6 red + 12 blue.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Distribution connects multiplication and addition—the bridge between operations.

Common stuck point: Works forwards (distributing) and backwards (factoring): ab + ac = a(b+c) is equally valid.

Sense of Study hint: Draw a box split into two parts to visualize how the outer factor multiplies each piece inside the parentheses.

Worked Examples

Example 1

easy
Expand 4(x + 7).

Solution

  1. 1
    Identify the two terms inside the parentheses: x and 7.
  2. 2
    Distribute 4 to each term inside the parentheses: 4 \cdot x + 4 \cdot 7.
  3. 3
    Simplify: 4x + 28.

Answer

4x + 28
The distributive property states a(b + c) = ab + ac. Multiply the outside factor by each term inside the parentheses.

Example 2

medium
Expand and simplify 3(2x - 5) + 2(x + 4).

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
Expand -2(3a - 4b + 1).

Example 2

easy
Use the distributive property to compute 6 \times 48 mentally.
← Back to Distributive Property Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

multiplicationaddition