Clear explanations and worked examples for every core algebra topic - from basic expressions to polynomial factoring. Useful whether you're working through homework or need a quick formula lookup. Variables, like terms, the distributive property, and one-step and two-step equations. What they are, the different types, and how to add, subtract, multiply, and evaluate them. Degree, standard form, adding, subtracting, and multiplying polynomials with examples. GCF, difference of squares, trinomial factoring, grouping, and sum/difference of cubes. What is Algebra? Algebra is the branch of mathematics that uses letters and symbols to represent numbers and quantities in formulas and equations. Unlike arithmetic, which works with specific known numbers, algebra works with general relationships that hold true for any value of the variable. It is a foundation for almost all of higher mathematics, including calculus, statistics, and physics. Mastering algebra means you can model real-world situations with equations and solve them systematically. The word itself comes from the Arabic "al-jabr," a term used in a 9th-century mathematics text to describe balancing an equation by moving a term from one side to the other. That's still exactly what solving an equation means today - keeping both sides balanced while you isolate the variable. Algebra vs. Arithmetic: What's the Difference? Arithmetic and algebra both use numbers and the same four basic operations, but they answer different kinds of questions: In practice, algebra is built entirely on arithmetic - every step of solving an equation is still just addition, subtraction, multiplication, and division. Algebra just organizes those operations around a variable instead of a single fixed answer. Why Learn Algebra? Algebra shows up everywhere: calculating discounts and interest rates, writing code, understanding scientific formulas, and solving engineering problems. Even if you never need to factor a polynomial again after school, the logical thinking skills that algebra builds are genuinely useful. More specifically, algebra trains you to break a problem into known and unknown parts, write a relationship between them, and work backward to find the unknown. That single skill - translate a real situation into an equation, then solve it - is the actual reason schools spend years on it, far more than any specific formula you'll memorize. Key Algebra Vocabulary A lot of algebra confusion comes down to not knowing what the words mean yet, not the math itself. Here are the terms you will see on every topic page in this section: Keep this table open in another tab the first few times you read a new topic page - most explanations lean on these words without re-defining them every time. How to Solve Word Problems Word problems feel harder than equations that are already written out, but the difficulty is almost always translation, not math. The process is the same every time: Identify what's unknown and assign it a variable. Find the relationship described in the words - look for phrases like "more than," "total," "twice," or "split evenly." Write the equation using that relationship. Solve using the same steps as any other equation. Check the answer makes sense in the context of the original question, not just algebraically. Worked example: "Sarah has $15 more than twice what Ben has. Together they have $60. How much does Ben have?" Ben has $15, and Sarah has 2(15) + 15 = $45. Check: 15 + 45 = 60. It matches the total given in the problem, so the answer is correct. Types of Algebraic Equations Not every equation is solved the same way. Recognizing the type tells you which method to reach for: This section covers linear equations, polynomials, and factoring in depth. Systems of equations and inequalities are related topics that build on the exact same balancing principle. Order of Operations Refresher Before solving any equation, you need to evaluate expressions in the right order. Algebra follows the same order of operations as arithmetic, usually remembered with the acronym PEMDAS : Worked example: to evaluate 3 + 2 × (4 + 1)² , first solve the parentheses (4 + 1 = 5), then the exponent (5² = 25), then the multiplication (2 × 25 = 50), and finally the addition (3 + 50 = 53). Skip a step out of order and you'll land on the wrong answer even if every individual calculation was correct. Algebra Signs & Symbols Reference A handful of symbols show up constantly once equations get more advanced. Here's what each one means: Step-by-Step Worked Examples Reading a formula is one thing - actually solving with it is another. Here are four common problem types, solved fully. Example 1: One-step equation Solve for x: x + 9 = 14 Example 2: Two-step equation Solve for x: 3x - 4 = 11

Example 3: Simplifying an expression Simplify: 4x + 7 - 2x + 3 Example 4: Factoring a simple trinomial Factor: x² + 5x + 6 Check any factoring answer by expanding it back out: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6. It matches, so the factoring is correct. Practice Problems Try solving these on paper first, then click each one to reveal the answer and check your work. Common Algebra Formulas Cheat Sheet A quick-reference version of the formulas covered in full depth on the Basic Algebra Formulas page: Common Mistakes to Avoid Quick Tips for Getting Algebra Right Algebra in Real Life Algebra stops feeling abstract once you notice it's already how you solve everyday problems: Splitting a bill or a game's high score. If three friends split a $45 pizza evenly, you're solving 3x = 45 for x - that's a one-step equation. Planning a trip. Distance = speed × time is an algebra formula. Knowing the distance and your average speed, you can solve for how long the drive will take. Saving up for something. If you save $8 a week and want $120, the equation 8x = 120 tells you it'll take 15 weeks. Discounts and sales tax. A 20% discount on a $60 item is the expression 60 - (0.20 × 60), the same kind of order-of-operations problem covered above. Video game stats. Damage-per-second, leveling curves, and crafting-material ratios in most games are just algebraic formulas with the variable names swapped for game terms. Cooking and baking. Doubling a recipe that calls for 3/4 cup of flour per batch means solving 2 × (3/4), the same fraction-and-multiplication reasoning used in algebraic expressions. Comparing phone or streaming plans. "Plan A costs $10 plus $2 per gigabyte, Plan B costs a flat $25" is two linear equations - setting them equal to each other tells you exactly where one plan becomes cheaper than the other. Frequently Confused Terms A few word pairs trip students up specifically because they sound similar but mean different things: Suggested Learning Path If you're working through this section from scratch, going in this order tends to build cleanly on what came before, rather than jumping into a topic that assumes knowledge you don't have yet: Vocabulary first. Get comfortable with variable, term, coefficient, expression, and equation before touching any formulas - see the table above. Algebra Basics . Like terms, the distributive property, and one-step and two-step equations - this is where the balancing method from the worked examples above gets real practice. Algebraic Expressions . Go deeper on building, simplifying, and evaluating expressions, and keep the basic algebra formulas page handy as a reference. Polynomial Definition . Once equations feel comfortable, learn to recognize degree, standard form, and how to add/subtract/multiply polynomial expressions. Factoring Polynomials . The most advanced topic here - reversing multiplication to break a polynomial into simpler pieces, building directly on everything above. When you are ready to test yourself, try the Linear Equations Quiz , then the full Algebra 1 Quiz . Tools That Help While You Practice SolveCalc's calculator has a few features built specifically for working through algebra problems, not just arithmetic: CalcSolver Code Mode Guide lets you type expressions like sqrt(16) or 2^10 directly with your keyboard instead of clicking buttons, which is much faster for checking a multi-step problem. The Equation Solver walks through solving a linear equation step by step, useful for confirming your own working matches the correct method, not just the correct final answer. The Exponent Calculator and Fraction Calculator handle the arithmetic sub-steps (powers, fractions) that show up constantly inside larger algebra problems, so an arithmetic slip doesn't get mistaken for an algebra mistake. A Few More Terms You'll Meet Soon These aren't covered in depth on this page, but they show up right after the basics above, so it helps to recognize them early: How to Use This Section Each topic page above covers one area in depth with a clear definition, worked examples, and common mistakes to avoid. Use the calculator on the home page to check your working as you go through the examples. Algebra rewards steady, small-step practice far more than trying to absorb everything in one sitting. Work through the vocabulary, try the practice problems above without looking at the answers first, and move on to one topic page at a time in the suggested order. The concepts genuinely do click once you've written out enough of your own worked examples by hand - and every formula on this page will still be here to reference whenever you need a refresher. Frequently Asked Questions