How to simplify algebraic expressions
Quick answer
First remove brackets by multiplying them out (the distributive property). Then combine like terms, meaning terms with exactly the same variable and power, by adding their coefficients. For example, 3x + 5 + 2x − 3 simplifies to 5x + 2.
Step by step
- Expand the bracketsMultiply the number outside a bracket by every term inside it. 2(x + 4) becomes 2x + 8.
- Group like termsGather terms with the same variable and power, for example all the x terms, all the x² terms, and all the plain numbers.
- Combine themAdd or subtract the coefficients of each group. 2x − 3x becomes −x.
- Write the answer neatlyList terms from the highest power down, with the plain number last.
Simplifying doesn’t change what an expression is worth. It just writes the same thing with fewer pieces, which makes the next step, often solving an equation, much easier.
What are like terms?
Like terms have the same letters raised to the same powers. Only the number in front, the coefficient, can differ.
| Like terms | Not like terms |
|---|---|
| 3x and −7x | 3x and 3x² |
| 4y² and y² | 4y and 4x |
| 5 and −12 | 5 and 5x |
Example 1: Combining like terms
3x + 5 + 2x − 3
x terms: 3x + 2x = 5x
Numbers: 5 − 3 = 2
Answer: 5x + 2
Example 2: Brackets first
2(x + 4) − 3x
Expand: 2x + 8 − 3x
Combine: 2x − 3x = −x
Answer: −x + 8
Example 3: Powers
4x² + 3x − x² + 2x
x² terms: 4x² − x² = 3x²
x terms: 3x + 2x = 5x
Answer: 3x² + 5x
Multiplying terms with exponents
When you multiply, add the exponents of the same letter and multiply the numbers:
- x² · x³ = x⁵
- (3x²)(2x) = 6x³
Adding is different: x² + x³ can’t be combined, because they aren’t like terms.
Watch the minus sign
A minus in front of a bracket changes the sign of everything inside:
−(2x − 5) = −2x + 5
Forgetting to flip the second sign is the single most common simplifying mistake. Once you’re comfortable with expressions, the same habits help with graphing inequalities on a number line.
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