Algebraic Expressions: Simplifying and Evaluating
Learn terms, coefficients, variables, like terms, and substitution with simple examples.
Quick Answer
3x + 2 − x + 5 = 2x + 7When to Use This
Simplifying an expression preserves its value for every allowed input. Evaluating an expression produces a number after a value is supplied. Neither task is the same as solving an equation: an expression on its own has no equals sign and does not determine x.
Step-by-Step Method
- Group terms with exactly the same variable part.
- Add or subtract their coefficients while retaining the variable.
- Combine the constants separately.
- If an input value is given, substitute it with parentheses and follow operation order.
Calculator Tips and Limits
- The linked page is a longer expression guide, not an automatic symbolic simplifier.
- Use the main scientific calculator to check numerical evaluations after substituting the variable yourself.
Worked Examples
Simplify, then substitute
In 3x + 2 - x + 5, the x coefficients are 3 and -1, so their total is 2. The constants total 7. The simplified form is 2x + 7. At x = -2, it evaluates to 2 × (-2) + 7 = 3.
Unlike powers stay separate
4x² + 3x - x² simplifies to 3x² + 3x. The squared and unsquared variable parts cannot be combined into 6x or 6x².
Common Mistakes
Treating x and x² as like terms
Matching letters are not enough: the exponents must match as well.
Dropping parentheses around a negative input
For x² with x = -2, evaluate (-2)² = 4. The expression -(2²) is a different expression and equals -4.
FAQ
Can an expression have more than one simplified form?
Yes. Factored and expanded forms can be equivalent and useful for different purposes.
How do I check that two forms agree?
Substituting several values can catch mistakes, but algebraic transformations are needed to establish equality for every permitted value.
References and corrections
OpenStax: Algebra and Trigonometry 2e — further reading. The worked examples on this page are CalcSolver explanations. Read our calculation and correction method, or report an error with the input and expected result.