LEMMA

Algebra basics

Combine like terms

ALEKS placementTEAS math

Terms combine only when the variable part matches exactly.

What this covers

  • Rewrite subtraction as adding a negative so each term carries its own sign.
  • Group terms with identical variables and exponents.
  • Add the coefficients; the variable part never changes.
  • Order the result by descending power.

Worked example

Worked example

Simplify 4x² - 3x + 7 - x² + 5x.

  1. (4x2−x2)+(−3x+5x)+7Group matching variable parts.
  2. 3x2+2x+7Add coefficients only.
Another worked example

Simplify 5x + 4 − 2x + 7.

  1. 5x+4+(−2)x+7The subtraction gives the second x term a coefficient of negative 2.
  2. (5+(−2))x+(4+7)Group matching x terms and keep the constants in a separate group.
  3. 3x+(4+7)Add only the signed x coefficients first; keep the variable part x.
  4. 3x+11Now add the constants separately.

A common mistake

A mistake Lemma catches

From (4x2−x2)+(−3x+5x)+7

3x4+2x+73x2+2x+7

“4x² and -x² became 3x^4 — adding like terms adds their coefficients and keeps the power the same; the exponents add only when terms are multiplied.”

Try one

Sample problem

Combine like terms.

2x+6+7x−4

Practice like terms free

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Where this fits

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