Method · Algebra
How to Simplify an Expression: Step by Step
Two moves, always in the same order: distribute what is in parentheses, then add up the coefficients of every matching power of x.
The two-step method
Every polynomial simplifies the same way, in this order.
- Distribute — multiply everything inside each set of parentheses by whatever sits outside it.
- Combine like terms — add the coefficients of every term sharing the same power of x.
Skipping straight to combining before distributing is the single most common way to get a wrong answer that still looks plausible.
Distributing a single term
- 3(2x + 1) − 4xthe expression
- 6x + 3 − 4xdistribute the 3 across both terms inside
- 2x + 3combine 6x and −4x, the only like terms
Only one pair of like terms exists here — the two x terms — so combining is a single subtraction once distribution is done.
Distributing a negative number
- −2(3x − 1)the expression
- −6x + 2the negative flips the sign of both terms inside
Distributing across two sets of parentheses
- 2(x − 3) + 3(x + 1)the expression
- 2x − 6 + 3x + 3distribute each term separately
- 5x − 3combine the x terms, then the constants
Each set of parentheses distributes independently — there is no interaction between them until the combining step, which gathers every like term from both at once.
Multiplying two parentheses together
- (x + 2)(x + 5)the expression
- x·x + x·5 + 2·x + 2·5distribute every term in the first bracket across every term in the second
- x² + 5x + 2x + 10multiply each pair out
- x² + 7x + 10combine the two x terms
Every term in the first parentheses has to reach every term in the second — four multiplications in total for two two-term brackets, not two.
When terms cancel completely
- 4(x − 1) − 2(x − 1)the expression
- 4x − 4 − 2x + 2distribute both terms
- 2x − 2combine like terms
A different pair of coefficients here could cancel entirely down to 0 — that is a correct, complete answer, not a sign that something went wrong partway through.
Checking your answer, always
Check your answer by substituting a value for x into both the original and the simplified expression. The two results must match exactly, whichever number you pick — if they disagree even once, a term was distributed or combined incorrectly somewhere.
The Simplify Calculator on this site runs this exact check internally, at several values of x, before showing a result — and withholds the answer rather than showing one that does not check out.
Vocabulary this method leans on
The distributive property is the name for the first step — a number outside parentheses reaching every term inside. To expand an expression means exactly this: apply the distributive property until no parentheses remain.
The degree of a term is the power of x it carries — 3x² has degree 2, and a constant term, a bare number with no x, always has degree 0. Combining is only ever valid between terms sharing the same degree, which is why a negative sign in front of a term has to travel with it through both distributing and combining, never left behind or applied to the wrong term.
None of this changes the order of operations already familiar from arithmetic — what sits inside parentheses is still resolved relative to that grouping first. Simplifying is that same rule, applied to an expression with a variable in it instead of only numbers.
Questions about how to simplify an expression
What is the first step in simplifying an expression?
Distribute any parentheses — multiply everything inside by whatever sits outside — before attempting to combine any terms.
What is 3(2x + 1) − 4x simplified?
2x + 3. Distribute to get 6x + 3 − 4x, then combine the two x terms.
Why does distributing a negative number flip both signs?
Because multiplying by a negative number reverses the sign of whatever it multiplies. −2(3x − 1) distributes to −6x + 2 — both terms flip.
How do I check a simplification is correct?
Substitute the same number for x into both the original and the simplified expression. They must produce the exact same result for the simplification to be correct.