Combining Like Terms
To simplify an expression, combine like terms — add or subtract the coefficients of terms that share the same variable and exponent.
This is a free explanation of Combining Like Terms — a preview, not the full interactive lesson. The lesson, practice, quizzes, and AI Tutor are inside the app.
Like terms are terms that have the exact same variable raised to the exact same exponent. Both conditions must be true — variable AND exponent. So 3x and 5x are like terms, and −2y² and 7y² are like terms, but 3x and 3x² are not, because their exponents differ.
To combine like terms, add or subtract their coefficients. Think of it this way: 3x means “3 of something” and 5x means “5 of the same something,” so together they make 8x. You cannot do the same with 3x and 3x², because x and x² are different “somethings.”
Two things students overlook: the coefficient of x is 1 and the coefficient of −x is −1 (never drop the sign). And terms can cancel to zero — 5y − 5y = 0, so that term disappears entirely. Unlike terms are never dropped; they simply stay side by side.
Worked example
Simplify: 3x + 5 − x + 2
- Sort the terms into groups by type: 3x and −x are like terms; 5 and 2 are like terms (both constants).
- Combine the x terms. The coefficient of −x is −1, so 3 + (−1) = 2. That gives 2x.
- Combine the constants: 5 + 2 = 7.
2x + 7
On the test: GED & HiSET questions ask you to simplify expressions before evaluating or solving them.
This concept also comes up in Polynomials.
Inside the app, Combining Like Terms comes with:
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- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
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