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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 both terms in the group

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

The distributive property multiplies the outside factor 3 by every term inside the parentheses.

02

Evaluate each product

\[3~\cdot~x~=~3x~\text{and}~3~\cdot~4~=~12\]

The variable product is 3x and the constant product is 12.

03

Write the expanded expression

\[3x~+~12\]

Adding the two partial products gives an expression equivalent to the original group.

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Another way

  1. Interpret the expression as three copies of x + 4; combining three x's and three 4's gives 3x + 12.

!

Common mistake

Do not multiply 3 by only x. The factor outside the parentheses must also multiply 4.

Solution walkthrough video