Combining Like Terms - Algebra Step by Step

Simplify a polynomial expression by adding together all terms with the same variable part.

combine-like-terms Like terms share the same variable and exponent. Add their coefficients; keep the variable part unchanged. 3x + 2x + x = (3 + 2 + 1)x = 6x

Example

Group matching variable terms and add their coefficients. Terms are like only when they share the same variable raised to the same power, so they count the same kind of quantity and can be merged. Adding their coefficients is really the distributive property in reverse, combining repeated copies of one quantity into a single, shorter term.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

3x + 2x - 5 +x

Step 2 — Group like terms

Group the x terms: 3x and 2x.

( \hlmath{3x} + \hlmath{2x} +x)- 5

Step 3 — Add coefficients

Add coefficients: 3 + 2 + 1 = 6.

( 3 + 2 + 1 )x= \hlmath{6x}

Step 4 — Result

Read the final result.

6x - 5