Expressions

Combining Like Terms

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

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+x3x + 2x - 5 +x
Sort terms by what kind of term they are.3xx term2xx term-5constantxx termadd coefficientswait until x terms are groupedresult--

Step 2 — Group like terms

Group the x terms: 3x and 2x.

(3x+2x+x)−5( \hlmath{3x} + \hlmath{2x} +x)- 5
Group the like x terms; the constant stays separate.3xx term2xx term-5constantxx termlike x termsconstant stays separateadd coefficientswait until x terms are groupedresult--

Step 3 — Add coefficients

Add coefficients: 3 + 2 + 1 = 6.

(3+2+1)x=6x( 3 + 2 + 1 )x= \hlmath{6x}
Add coefficients: 3 + 2 + 1 = 6.3xx term2xx term-5constantxx termlike x termsconstant stays separateadd coefficients3 + 2 + 1 = 6result--

Step 4 — Result

Read the final result.

6x−56x - 5
Result: 6x - 5.3xx term2xx term-5constantxx termlike x termsconstant stays separateadd coefficients3 + 2 + 1 = 6result6x - 5
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