Simplify Calculator

Type one expression, click Calculate. This simplify calculator returns the simplest form instantly, right on the page.

• Expression to simplify — any algebraic expression, no = sign needed. The box starts preloaded with $2(x + 3) - 4$; press Calculate and the simplify calculator answers $2x + 2$.
• The example chips under the box load ready-made inputs: $(x^2 - 9)/(x + 3)$ for cancelling factors, $3x + 2x - 5$ for like terms, and $x^2 + 5x + 6$ for an expression that is already simple.
• Press Calculate and the simplified form comes back in one line — $2x + 2$ for the preloaded expression.

Simplifying is not solving: there is no $x =$ at the end, only a shorter expression worth exactly the same as the one you typed.

This page is more than a static simplify calculator — it is also an AI tutor you can ask questions:

• Ask in plain words. “Simplify two times the quantity x plus 3, minus 4” — the AI turns the sentence into $2(x + 3) - 4$ and simplifies it step by step.
• Take a photo of your homework. No typing: the AI reads the expression straight off the page and simplifies it step by step.
• Ask about the ideas, not just the answer. “Why can I not cancel the x on top with the x on the bottom?” The AI explains the rule — and you can check every result against the simplify calculator on this page, so nothing is guessed.
• Work backwards, then keep asking. Give the AI a simplified answer and ask which expressions produce it. Follow-ups are welcome, so ask “why?” as often as you need: this simplify calculator page keeps teaching.

To simplify an expression is to rewrite it in the shortest form that is equivalent — worth exactly the same as the original for every value of the letter, only shorter to read and easier to use.

Equivalence is the load-bearing word. $2(x + 3) - 4$ and $2x + 2$ are the same expression in different clothes: expand the brackets and $2x + 6 - 4$ collects to $2x + 2$. Nothing was solved, because there was nothing to solve — no equation, no = sign, no unknown to pin down. The simplify calculator answers a different question than a solver does: not “what is x?” but “can this be said more briefly?”

Why bother? Because short expressions make everything downstream easier. An answer of $2x + 2$ is quicker to graph, quicker to substitute into, and quicker to compare with a classmate's. Teachers ask for answers in simplest form for the same reason editors ask for short sentences: the shortest version is the easiest to check.

The moves available are exactly three, and the rest of this page walks each one: combine like terms, expand brackets and collect, and cancel common factors in a fraction. The simplify calculator above applies all three, in whichever order the expression needs.

Like terms are terms with the same letter raised to the same power. $3x$ and $2x$ are like terms — both count x's — so they combine to $5x$ exactly as 3 apples plus 2 apples makes 5 apples.

$x$ and $x^2$ are not like terms. One counts x's, the other counts squares of x, and no amount of collecting turns one into the other. An expression such as $x^2 + 5x + 6$ is already fully simplified for exactly this reason: three unlike terms, nothing left to combine.

The rule in symbols:

$3x + 2x = 5x$

$3x^2 + 2x = 3x^2 + 2x \quad \text{(already simplest)}$

Numbers standing alone are like terms with each other. In $3x + 2x - 5$, the $3x$ and $2x$ combine to $5x$ while the $-5$ waits, untouched, in the final answer $5x - 5$.

A quick self-check when combining: count your terms before and after. Combining like terms can only shrink the count — if your answer has more terms than the input, something was merged that should not have been. The simplify calculator above never merges unlike terms, which is why its output is safe to trust as simplest form.

Brackets first, then collect. The preloaded example shows the whole routine in one line:

$2(x + 3) - 4 = 2x + 6 - 4 = 2x + 2$

1. Expand. The 2 outside multiplies every term inside: $2(x + 3) = 2x + 6$ — both the $x$ and the 3.
2. Collect like terms. $2x$ has no partner, but $6 - 4$ are plain numbers: they combine to 2.
3. Read the result. $2x + 2$ is the simplest form — two unlike terms, nothing further to do.

The order is not negotiable: the $-4$ cannot combine with anything until the brackets are gone, because before expanding, the $+3$ is locked inside. Expanding is the key that unlocks the door.

Distribution slips are the most expensive kind, because they happen on line one and poison everything after. $2(x + 3)$ is $2x + 6$, never $2x + 3$ — the outside number multiplies the inside number as well as the letter. Type the original expression into the simplify calculator above and compare line by line with your notebook; the two should agree at every step.

Fractions cancel by factors, never by terms. A factor is something the whole numerator is multiplied by; a term is one piece added to the rest. The simplify calculator above draws that line precisely, and $(x^2 - 9)/(x + 3)$ — the second example chip in its box — shows why the line matters:

$\dfrac{x^2 - 9}{x + 3} = \dfrac{(x - 3)(x + 3)}{x + 3} = x - 3$

1. Factor the top completely. $x^2 - 9$ is a difference of squares: $(x - 3)(x + 3)$.
2. Spot the common factor. $x + 3$ now sits above and below the fraction bar, as a factor of each whole side.
3. Cancel it. A nonzero number divided by itself is 1, so the fraction collapses to $x - 3$.

One footnote matters: the cancellation holds for $x \neq -3$, because at $x = -3$ the original fraction has a zero denominator. In simplest-form work the convention is to report the result as $x - 3$ with that fact understood.

What you may not do is cross out single terms — the $x^2$ against the $x$, or the $9$ against the $3$. Cancelling is legal only between factors of the entire top and the entire bottom; the mistakes section below returns to this, because it is the most common simplifying error of all.

Simplify $3x + 2x - 5$. No brackets, no fractions — this one is pure like-term collecting:

1. Identify the like terms. $3x$ and $2x$ share the same letter to the same power, so they combine. The $-5$ is a constant with no partner.
2. Combine them. $3x + 2x = 5x$.
3. Carry the lonely term along. The answer is $5x - 5$.

Reading it aloud helps: “three x's plus two more x's, minus 5” is “five x's, minus 5”. The expression got shorter by one term and changed not at all in value.

Notice what a finished simplification looks like: every letter appears once, every bracket is gone, and no fraction hides a common factor. The simplify calculator above applies that same checklist — feed it $(x^2 - 9)/(x + 3)$ and it runs the factor-and-cancel route from the previous section; feed it $2(x + 3) - 4$ and it runs expand-and-collect. One box, three moves, picked to fit the input.

If your hand result and the simplify calculator's line ever disagree, re-check the middle step: the error is almost always a term that was combined, dropped, or cancelled when it should have been left alone.

Three errors the simplify calculator sees every day. In each one the tool stays right and the handwriting goes wrong:

1. Cancelling terms instead of factors. In $\dfrac{x^2 - 9}{x + 3}$ you cannot cross out the $x^2$ against the $x$, or the $9$ against the $3$. Cancelling is legal only for a factor shared by the whole top and the whole bottom — which is why the correct route factors $x^2 - 9$ into $(x - 3)(x + 3)$ first.
2. Combining unlike terms. $x + x^2$ does not merge into one term; different powers are different objects. An expression like $x^2 + 5x + 6$ is already in simplest form, and forcing a combination produces a different expression entirely — one that is not equivalent to the original.
3. Distributing to only one term inside the brackets. $2(x + 3)$ is $2x + 6$, not $2x + 3$ — the outside multiplier reaches every term inside. A slip here corrupts every line below it.

The defence against all three is the same: read the final expression and ask whether it is equivalent to what you started with. The simplify calculator above asks that question on every run — and unlike the memory of last night's homework, it never tires of the answer.