Simplifying an algebraic expression means rewriting it in its shortest, cleanest form without changing its value. It is the first skill behind solving equations, factoring, and graphing. You can check your work with the free tools on Calc Solver.
What Simplifying Means
An expression like 3x + 2x + 5 – 2 looks messy, but it hides a simpler form. Simplifying collects everything that can be combined and removes anything unnecessary, so the expression becomes easier to read and use.
Step 1: Remove Parentheses
Start by expanding any brackets. Multiply each term inside by the number outside: 2(x + 3) becomes 2x + 6. Watch the signs carefully, because a minus sign in front of brackets flips every sign inside: -(x – 4) becomes -x + 4.
Step 2: Combine Like Terms
Like terms have exactly the same variable part. The terms 3x and 2x are like terms, but 3x and 3x^2 are not. Add or subtract their coefficients: 3x + 2x + 5 – 2 becomes 5x + 3. Constants combine only with constants, and x terms only with x terms.
Step 3: Apply Exponent Rules
When the same base is multiplied, add the exponents: x^2 times x^3 is x^5. When it is divided, subtract them: x^5 divided by x^2 is x^3. Do not add exponents when terms are added: x^2 + x^2 is 2x^2, not x^4.
Worked Example
Simplify 3(x + 2) + 2x – 4. First expand: 3x + 6 + 2x – 4. Then combine like terms: 3x + 2x is 5x, and 6 – 4 is 2. The simplified form is 5x + 2. Substitute a value, for example x = 1, into both the original and the simplified form to confirm they match: both give 7.
Common Mistakes to Avoid
First, combining terms that are not alike, such as adding x and x^2. Second, forgetting to distribute a number or a minus sign to every term inside brackets. Third, changing the value by dropping a term instead of combining it. A quick substitution check catches all three.
Practice Problems to Try
Simplify 4x + 3 – 2x + 7, then 2(3x – 1) + 5x, then x^2 + 3x – x^2 + 2x. Check each answer by substituting x = 2 into both forms.