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All courses Math Foundations · MF.EQ.3 30 of 60
Combine like terms and simplify expressions while preserving structure.

Combine like variable terms

Problem
Simplify the expression \(3x~+~5x\).
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Hint

Look at the two terms and notice they both have the same variable part: x.

These are like terms, so you add the coefficients and keep the x attached.

Solution walkthrough

01

Identify the like terms

\[3x~\text{and}~5x~\text{both}~\text{have}~\text{variable}~\text{part}~x\]

Terms are like terms when their variable parts match exactly, so these coefficients can be combined.

02

Add the coefficients

\[3x~+~5x~=~(3~+~5)x\]

Three copies of x plus five copies of x make eight copies of the same quantity.

03

Write the simplified expression

\[8x\]

The coefficient sum is 8 and the common variable factor remains x.

+

Another way

  1. Factor out x: 3x + 5x = x(3 + 5) = 8x.

!

Common mistake

Do not drop x or multiply x by itself. Combining like terms adds 3 and 5; it does not create x squared.

Solution walkthrough video