Enter your algebraic expression below. The calculator will attempt to simplify it.
Your simplified expression will appear here.
Understanding Algebraic Expression Simplification
Algebraic expressions are combinations of numbers, variables (like x, y, z), and mathematical operations (addition, subtraction, multiplication, division). Simplifying an algebraic expression means rewriting it in a more concise form without changing its value. This is a fundamental skill in algebra used to make equations easier to solve and understand.
Key Principles for Simplification:
Combining Like Terms: This is the most common method. Like terms are terms that have the same variables raised to the same powers. For example, 3x and -2x are like terms, but 3x and 3x² are not. To combine like terms, you add or subtract their coefficients (the numbers in front of the variables).
Example: 5x + 2y - 3x + 4y can be simplified by grouping like terms: (5x - 3x) + (2y + 4y) which results in 2x + 6y.
Distributive Property: This property is used when you have a number or variable multiplying a group of terms inside parentheses. For example, a(b + c) = ab + ac.
Example: Simplify 3(x + 2y) - 2(x - y).
Using the distributive property: 3x + 6y - 2x + 2y.
Now, combine like terms: (3x - 2x) + (6y + 2y) which simplifies to x + 8y.
Order of Operations (PEMDAS/BODMAS): Ensure operations are performed in the correct order (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction). This is crucial when an expression involves multiple types of operations.
Why Simplify Expressions?
Easier Problem Solving: Simpler expressions are less prone to errors when solving equations or performing further calculations.
Understanding Relationships: Simplification can reveal the underlying structure and relationships between variables more clearly.
Foundation for Advanced Math: It's a prerequisite for higher-level mathematics, including calculus, linear algebra, and more complex equation solving.
How This Calculator Works:
This calculator uses a JavaScript-based approach to parse and simplify basic algebraic expressions. It identifies terms, groups them by variable (including constant terms), and applies the rules of combining like terms and the distributive property where applicable. Please note that for highly complex expressions involving exponents, fractions, or advanced functions, a dedicated symbolic math engine might be required.
function simplifyExpression() {
var expressionInput = document.getElementById("expression").value.trim();
var resultDiv = document.getElementById("result");
var errorMessageDiv = document.getElementById("error-message");
errorMessageDiv.innerText = ""; // Clear previous error messages
if (expressionInput === "") {
errorMessageDiv.innerText = "Please enter an algebraic expression.";
resultDiv.innerText = "Your simplified expression will appear here.";
return;
}
try {
// Basic simplification logic – this is a simplified parser and may not handle all cases.
// It focuses on combining like terms for linear expressions.
// For more advanced math, a dedicated library would be needed.
// Normalize: replace subtraction with addition of negative, remove spaces
var normalizedExpression = expressionInput.replace(/\s+/g, ").replace(/-/g, '+-');
// Split into terms
var terms = normalizedExpression.split('+').filter(function(term) {
return term !== " && term !== '-'; // Filter out empty strings and lone '-'
});
var coefficients = {}; // Store coefficients for each variable, plus a 'constant' key
terms.forEach(function(term) {
var variable = ";
var coefficientStr = '1'; // Default coefficient is 1
if (term.includes('x')) {
variable = 'x';
var parts = term.split('x');
if (parts[0] === " || parts[0] === '+') { // Handles 'x' or '+x'
coefficientStr = '1';
} else if (parts[0] === '-') { // Handles '-x'
coefficientStr = '-1';
} else {
coefficientStr = parts[0];
}
} else {
variable = 'constant'; // It's a constant term
coefficientStr = term;
}
var coefficient = parseFloat(coefficientStr);
if (isNaN(coefficient)) {
// This indicates an issue, like '2xx' or invalid input format.
// For robustness, we could throw an error or try to salvage.
// Here, we'll proceed but the result might be unexpected.
console.warn("Could not parse coefficient for term: " + term);
coefficient = 0; // Treat as zero if parsing fails
}
if (!coefficients[variable]) {
coefficients[variable] = 0;
}
coefficients[variable] += coefficient;
});
var simplifiedTerms = [];
var sortedVars = Object.keys(coefficients).sort(function(a, b) {
if (a === 'constant') return 1; // Constants go last
if (b === 'constant') return -1;
return a.localeCompare(b); // Alphabetical sort for variables
});
sortedVars.forEach(function(variable) {
var coeff = coefficients[variable];
if (coeff === 0) return; // Skip terms with zero coefficient
var termStr = ";
if (variable === 'constant') {
termStr = coeff.toString();
} else {
if (coeff === 1) {
termStr = variable;
} else if (coeff === -1) {
termStr = '-' + variable;
} else {
termStr = coeff + variable;
}
}
// Format the term for output, handling signs nicely
if (simplifiedTerms.length > 0 && coeff > 0) {
simplifiedTerms.push('+' + termStr);
} else {
simplifiedTerms.push(termStr);
}
});
var simplifiedExpression = simplifiedTerms.join(");
if (simplifiedExpression === "") {
simplifiedExpression = "0"; // If all terms cancelled out
}
resultDiv.innerText = simplifiedExpression;
} catch (e) {
console.error("Error during simplification: ", e);
errorMessageDiv.innerText = "Could not simplify the expression. Please check the format.";
resultDiv.innerText = "Error";
}
}