Collecting Like Terms
Simplify algebraic expressions by collecting like terms: combine terms with the same variable and power (e.g., 3a + 2b + 5a = 8a + 2b) while maintaining equivalence
What a learner can do afterwards
- Identify like terms in an algebraic expression
- Combine like terms involving positive and negative coefficients
- Simplify expressions involving multiple variables and constant terms
1 · Read
An expression can have several terms, like 3a + 2b + 5a. Some of these terms are like terms: they have the exact same variable raised to the same power. Only the coefficient, the number in front, can be different. 3a and 5a are like terms. 3a and 2b are not, because the letters are different.
Negative coefficients work the same way: add the signed numbers in front. In 7m - 2m + 4, 7 + (-2) = 5, giving 5m + 4. The answer can land below zero: for 3n - 5n, start at 3 and count 5 back, 2, 1, 0, -1, -2, so you get -2n. Two minus terms join: -2t - 4t = -6t. And -3q + q = -2q, since one step up from -3 is -2.
Only combine terms that match exactly: same letter, same power. Never fold a constant into a term that has a letter, and never multiply the letters together when you collect terms.
Collecting like terms means adding or subtracting the coefficients of terms that share the same variable and power, and leaving everything else untouched.
Readings 'Stacking like terms', 'Terms, coefficients and constants' and 'The language of algebra' are original to this dataset. All 12 extra questions are original to this dataset.
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