Combining like terms is a basic algebra skill that turns long expressions into simpler ones without changing their value. It works like sorting objects into matching groups before counting them. In algebra, the matching part is the variable part, such as x, y, or x^2.
This skill matters because simplifying expressions makes equations easier to solve and patterns easier to see.
Like terms have exactly the same variables raised to exactly the same powers, so 3x and -5x are like terms, but 3x and 3x^2 are not. When terms are like terms, you add or subtract only their coefficients and keep the variable part unchanged. Constants are also like terms with other constants because they have no variable part.
Before solving many equations, you first simplify each side by combining all like terms.
Key Facts
- Like terms have the same variable part, including the same exponents.
- To combine like terms, add or subtract the coefficients and keep the variable part the same.
- 3x + 5x = 8x
- 7a^2 - 2a^2 = 5a^2
- 4x + 3y cannot be combined because x and y are different variable parts.
- Constants combine with constants, so 9 - 4 + 2 = 7.
Vocabulary
- Term
- A term is a number, a variable, or a product of numbers and variables in an expression.
- Coefficient
- A coefficient is the number multiplied by a variable in a term.
- Variable
- A variable is a letter or symbol that represents a number that can change or be unknown.
- Like Terms
- Like terms are terms with exactly the same variable part and exponents.
- Simplify
- To simplify is to rewrite an expression in a shorter or clearer equivalent form.
Common Mistakes to Avoid
- Combining terms with different variables is wrong because 4x + 3y cannot become 7xy or 7x.
- Combining terms with different exponents is wrong because x and x^2 represent different variable parts.
- Adding variables instead of coefficients is wrong because 2x + 5x equals 7x, not 7x^2.
- Ignoring negative signs is wrong because the sign is part of the coefficient, so 6a - 10a equals -4a.
Practice Questions
- 1 Simplify: 8x + 3x - 5x.
- 2 Simplify: 4a^2 + 7a - 9a^2 + 2a + 6 - 1.
- 3 Explain why 5m + 2n cannot be combined into one term, but 5m + 2m can.