Algebra Solver
Evaluate expressions, substitute variables, expand algebraic identities, simplify, and find prime factorization — with complete step-by-step solutions.
f Formulas Used
? How To Use
★ Key Features
5 Algebra Modes
Evaluate, substitute, simplify, expand, and factor all in one tool.
Step-by-Step Working
Full solution shown for every calculation — ideal for homework checking.
Real-Time Results
Answers update instantly as you type values in the input fields.
Mobile Optimized
Clean, readable layout designed for comfortable use on any device.
✎ Real-World Example
Step 1: (x+5)² = x² + 2(x)(5) + 5²
Step 2: = x² + 10x + 25
Example with x=7: (7+5)² = 49 + 70 + 25 = 144 = 12² ✓
Q Frequently Asked Questions
Algebra Solver - Free Evaluate, Expand, Factor & Substitute Calculator
Algebra has a way of feeling like five completely different subjects crammed into one class — expanding brackets is one skill, substituting variables is another, and factoring feels like a third thing entirely, even though they're all technically "algebra." An algebra solver that actually separates these into distinct modes, rather than pretending they're one uniform skill, tends to make a lot more sense than a single generic calculator trying to guess what you're asking for.
What genuinely helps here isn't just getting a correct final number — it's seeing the specific method that applies to whatever you're working on. Expanding (a+b)² uses a completely different approach than substituting x=3 into an expression, which is different again from factoring 360 into its prime components. A tool built around five clearly separated modes means you're never accidentally applying the wrong method to the wrong kind of problem.
The Five Things This Tool Handles
Evaluate
This mode takes any numerical expression — something like 3² + 4×5 − (12/4) — and calculates it following standard order of operations (BODMAS/PEMDAS): brackets first, then exponents, then multiplication and division left to right, then addition and subtraction left to right. Getting this order wrong is genuinely one of the most common arithmetic mistakes people make, even well past school age.
Substitute
Here you write an expression using variables — x, y, z — and then plug in specific numbers for each one. An expression like 2x² + 3x − 5 becomes a concrete number once you tell the tool that x equals, say, 4. This is the exact skill that bridges basic arithmetic into actual algebra, since it's the first time a letter starts standing in for a number that can change.
Simplify
This mode evaluates numerical expressions and fractions, reducing them to their simplest form. Feed it 12/8 and it recognizes the fraction, finds the greatest common factor, and reduces it down to 3/2 rather than leaving you with an unsimplified answer.
Expand
Five common algebraic identities live here: (a+b)², (a-b)², (a+b)(a-b), (a+b)(c+d) via FOIL, and (a+b)³. Pick a formula, plug in values for a and b (or all four letters for FOIL), and watch the full expansion play out with every intermediate step shown.
Factor
Enter any whole number and this mode breaks it down into its prime factorization, lists every single factor, and shows the factor pairs. 360, for instance, breaks down into 2³ × 3² × 5 — information that's genuinely useful well beyond a single homework problem.
Algebra Solver — Key Formulas
| Type | Formula |
|---|---|
| Linear equation | ax + b = 0 → x = −b/a |
| Quadratic formula | x = (−b ± √(b²−4ac)) / 2a |
| Square of sum | (a+b)² = a² + 2ab + b² |
| Square of difference | (a−b)² = a² − 2ab + b² |
| Difference of squares | a² − b² = (a+b)(a−b) |
How to Use This Algebra Solver
- Pick a tab based on what you actually need — Evaluate, Substitute, Simplify, Expand, or Factor
- For Evaluate or Simplify, type your expression using +, -, *, /, ^, and parentheses directly
- For Substitute, write your expression with x, y, or z as variables, then fill in their values separately
- For Expand, choose one of the five identity buttons, then enter values for a and b (and c, d if you're using FOIL)
- For Factor, just type a whole number and the prime factorization, all factors, and factor pairs appear instantly
Real Example: Expanding a Garden's Area
Say a square garden has a side length of (x + 5) meters, and you need the area expressed algebraically before plugging in an actual number.
Area = (x+5)², which follows the (a+b)² identity where a=x and b=5. Expanding gives: (x+5)² = x² + 2(x)(5) + 5² = x² + 10x + 25.
Now plug in an actual value — say x = 7: (7+5)² = 49 + 70 + 25 = 144, which also checks out as 12² exactly. That's the entire point of expanding first: once you have the algebraic form worked out, testing it against any specific number becomes trivial.
Algebra Solver — Solved Examples
| Equation | Solution |
|---|---|
| 2x + 5 = 15 | x = 5 |
| 3x − 7 = 8 | x = 5 |
| x² − 5x + 6 = 0 | x = 2, 3 |
| x² − 9 = 0 | x = 3, −3 |
| 2x² + 3x − 2 = 0 | x = 0.5, −2 |
Why Expanding Identities Actually Matters
It's tempting to think memorized identities like (a+b)² are just a school exercise, but they show up constantly once you start looking for them. Squaring a binomial expression, working out compound interest formulas, or simplifying physics equations involving squared terms all lean on the exact same (a+b)² = a² + 2ab + b² pattern. Recognizing that pattern instantly, rather than expanding everything from scratch each time, is genuinely one of the more useful algebra shortcuts to internalize.
Order of Operations Deserves Its Own Attention
BODMAS (or PEMDAS, depending on where you learned it) isn't just a rule for school exams — get the order wrong on a real calculation and the entire result changes. 3 + 4 × 5 isn't 35; it's 23, because multiplication happens before addition. This calculator applies the correct order automatically on the Evaluate tab, which is exactly the kind of detail that matters when you're double-checking a spreadsheet formula or a physics calculation rather than just a textbook problem.
Substitution Bridges Arithmetic Into Real Algebra
The moment a letter starts representing a number that can change is genuinely the moment arithmetic becomes algebra. Once substitution clicks, it opens the door to solving actual equations — which is where the Equation Solver picks up, handling linear equations, quadratics, and systems of two equations rather than just evaluating a single expression with known variable values.
Factoring Connects to Several Other Tools
Prime factorization isn't just an isolated skill — it's the foundation behind finding a greatest common factor or least common multiple. If you've factored a number here and need to compare it against another for GCF or LCM purposes, the GCF Calculator and LCM Calculator take that comparison further. And for double-checking whether a specific number is genuinely prime before factoring, the Prime Number Checker gives an instant yes-or-no answer with proof.
Where Algebra Connects to Fractions and Roots
Simplifying an expression sometimes produces a fraction that needs reducing, which is exactly what the Fraction Calculator handles directly. And if an expanded or factored expression involves squared or cubed terms that need reversing, the Square Root Calculator and Cube Root Calculator pick up exactly where basic algebra leaves off.
A Common Mistake in Expanding Brackets
One error that comes up constantly: forgetting the middle term when expanding (a+b)². It's tempting to assume (a+b)² just equals a² + b², skipping the 2ab entirely — but that's incomplete and mathematically wrong. The middle term exists precisely because expanding (a+b)(a+b) requires multiplying every term in the first bracket by every term in the second, and that cross-multiplication is exactly where 2ab comes from.
When Algebra Meets More Advanced Math
For calculations that go beyond simple expression evaluation — involving trigonometry, logarithms, or more complex scientific formulas — the Scientific Calculator extends the toolkit considerably. And for anything requiring grids of values rather than single expressions, the Matrix Calculator handles that entirely different category of algebraic work.
Frequently Asked Questions
What is the correct order of operations?
Brackets first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. This calculator applies that order automatically on the Evaluate tab for any expression you type.
What does (a+b)² expand to?
(a+b)² = a² + 2ab + b². For example, with a=3 and b=4: (3+4)² = 9 + 24 + 16 = 49, which matches 7² exactly.
How do I substitute values into an algebraic expression?
Write your expression using x, y, and z as variable names (using * for multiplication rather than writing 2x directly), then enter the numerical values for each variable and the tool computes the result.
How do I find the prime factorization of a large number?
Use the Factor tab and enter any whole number up to about 10 million — the tool returns the complete prime factorization, total factor count, and every factor pair instantly.
Is this algebra solver free to use?
Yes, completely free with no sign up required, working instantly on any device.
Explore more calculators: Equation Solver | Matrix Calculator | Fraction Calculator | Prime Number Checker
Reviewed by Kromo Tools Team
Building free, reliable online calculators and utilities for students, professionals, and everyday users. Last updated:
