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All courses Math Foundations · MF.EQ.4 31 of 60
Use the distributive property to expand and factor simple linear expressions.

Expand with distribution

Problem
Use the distributive property to expand 3(x + 4).
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Hint

Start by identifying the outside factor: 3. Multiply that 3 by each term inside the parentheses, beginning with x.

Use the distributive property: the number outside the parentheses must multiply both x and 4, not just the first term.

Solution walkthrough

01

Identify the outside factor

\[3(x~+~4)\]

The outside factor is 3. The distributive property means that 3 must multiply every term inside the parentheses, both x and 4.

02

Distribute to x

\[3~\cdot~x~=~3x\]

First multiply the 3 by the variable term x. That gives the first term of the expanded expression.

03

Distribute to 4

\[3~\cdot~4~=~12\]

Then multiply the same outside factor, 3, by the constant term 4. This is the part students sometimes forget.

04

Write the expression without parentheses

\[3(x~+~4)~=~3x~+~12\]

Combine the two distributed products. The expanded equivalent expression is 3x + 12.

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Another way

  1. Check by factoring the result: 3x + 12 = 3(x + 4), so the expansion matches the original expression.

!

Common mistake

A common mistake is writing 3x + 4. That multiplies 3 by x but leaves the 4 unchanged. In 3(x + 4), the 3 must be distributed to both terms inside the parentheses.