Algebraic Expressions
8 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team
An algebraic expression combines numbers, variables and operations without an equals sign, such as 4x + 3y − 2x + 7y. Being fluent at simplifying, evaluating and expanding expressions is the foundation for solving equations and factoring later. This guide covers each skill with worked examples.
Anatomy of an expression
In 4x + 3y − 2x + 7y there are four terms, separated by plus and minus signs. Each term has a coefficient (4, 3, −2, 7) and a variable part (x or y). Like terms have the same variable part and can be combined; unlike terms cannot.
Simplifying by combining like terms
Group the x-terms and the y-terms: (4x − 2x) + (3y + 7y) = 2x + 10y. The signs travel with the terms. Another example: 5a² − 2a + 3a² + a − 4 = 8a² − a − 4. Note that a² and a are different, so they stay separate.
Evaluating an expression
Replace each variable with its value and follow the order of operations. For 3a² − 2b + 1 with a = 2 and b = −3: 3(4) − 2(−3) + 1 = 12 + 6 + 1 = 19. Use brackets around negative values to avoid sign errors.
Expanding brackets
Single bracket: 4(2x − 3) = 8x − 12.
Two brackets (FOIL: First, Outer, Inner, Last): (x + 3)(x + 5) = x² + 5x + 3x + 15 = x² + 8x + 15.
Special products: (a + b)² = a² + 2ab + b², so (2x − 1)² = 4x² − 4x + 1. And (a + b)(a − b) = a² − b², so (x + 6)(x − 6) = x² − 36. Check with the polynomial calculator.
Common mistakes
- Adding unlike terms, such as writing 3x + 2y = 5xy.
- Squaring incorrectly: (x + 3)² is not x² + 9; it is x² + 6x + 9.
- Losing a negative sign when distributing: −(x − 4) = −x + 4.
- Forgetting that x × x = x², not 2x.
Practice questions
Test yourself, then tap to check. Answers are calculated by the tools linked below.
- Multiply (x + 3)(x − 5).
Show answer
Product: x² − 2x − 15
- Solve 4x − 3 = x + 12.
Show answer
x: 5
- Calculate 7^4.
Show answer
7^4: 2,401
Frequently asked questions
What are like terms?
Terms with exactly the same variables raised to the same powers, such as 3x² and −5x².
What does FOIL stand for?
First, Outer, Inner, Last: the four products you add when multiplying two binomials.
How do I simplify an expression?
Expand any brackets, then combine like terms.
Is (x + 3)² equal to x² + 9?
No. Expanding gives x² + 6x + 9, because you must include the middle term.
Try it yourself
Polynomial CalculatorAdd, subtract and multiply polynomials and evaluate the result at any x.Equation SolverSolve linear equations and 2×2 systems of equations with steps and a built-in check.Exponent CalculatorRaise any number to a power, including negative and fractional exponents.Keep learning
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