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Algebra › Expressions
Expressions
An expression is a phrase, not a sentence. It has no equals sign — just a value waiting to be calculated or simplified.
Combine like terms
Group same-letter terms — same colour, same family.
Original
3x+5+2x−1
Expression vs equation
- Expression:
3x + 5— has a value once you know x. - Equation:
3x + 5 = 14— has an equals sign and can be solved.
The parts
- Term — a single number, variable or product.
3x,5,−2y²are terms. - Coefficient — the number in front of a variable. In
3x, the 3 is the coefficient. - Constant — a plain number. In
3x + 5, 5 is the constant. - Like terms — terms with the same variable part.
3xand7xare like terms.
Combining like terms
You can add or subtract the coefficients of like terms.
3x + 7x = 10x5y − 2y = 3y4x + 5 + 2x − 3 = 6x + 2
You can't combine apples and oranges
3x + 5y stays as is. They aren't like terms — different letters mean different things.Expanding brackets
To expand 3(x + 4), multiply the 3 by everything inside: 3x + 12. This is the distributive law.
Quick check
- Simplify
5a + 3 − 2a + 4. - Expand
2(3y − 5). - What is the coefficient of x in
−7x?
Answers: 3a + 7, 6y − 10, and −7.
Quick check
Simplify 5a + 3 − 2a + 4.
Quick check
Expand 2(3y − 5).