Simplify Expression Calculator
Free Simplify expression Calculator for algebra. Enter values to get step-by-step solutions with formulas and graphs. Free to use with no signup required.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Combine like terms: ax + bx = (a+b)x | FOIL: (a+b)(c+d) = ac+ad+bc+bd
Simplification combines like terms (same variable and exponent), applies the distributive property to remove parentheses, and uses FOIL or the binomial theorem for products and powers of expressions.
Worked Examples
Example 1: Adding Two Linear Expressions
Problem:Simplify (3x + 2) + (5x - 4).
Solution:Remove parentheses: 3x + 2 + 5x - 4\nCombine x terms: 3x + 5x = 8x\nCombine constants: 2 + (-4) = -2\nSimplified: 8x - 2\nVerify at x=1: original = (3+2)+(5-4) = 5+1 = 6, simplified = 8-2 = 6
Result:Simplified: 8x - 2
Example 2: Multiplying Two Binomials Using FOIL
Problem:Expand and simplify (3x + 2)(5x - 4).
Solution:First: 3x * 5x = 15x^2\nOuter: 3x * (-4) = -12x\nInner: 2 * 5x = 10x\nLast: 2 * (-4) = -8\nCombine: 15x^2 + (-12x + 10x) + (-8)\nSimplified: 15x^2 - 2x - 8\nVerify at x=1: (5)(-2+4-8) wait... (3+2)(5-4) = 5*1 = 5, 15-2-8 = 5
Result:Simplified: 15x^2 - 2x - 8
Frequently Asked Questions
What does it mean to simplify an algebraic expression?
Simplifying an algebraic expression means rewriting it in a more compact or standard form by combining like terms, applying the distributive property, and reducing coefficients. Like terms are terms that have the same variable raised to the same power, such as 3x and 5x or 2x^2 and -7x^2. When simplifying, you add or subtract the coefficients of like terms while keeping the variable part unchanged. The goal is to reduce the expression to the fewest possible terms while maintaining mathematical equivalence. A fully simplified expression has no like terms remaining, no unnecessary parentheses, and all operations have been performed.
How do you simplify expressions involving exponents?
Exponent rules are essential for simplification. The product rule states x^a * x^b = x^(a+b). The quotient rule states x^a / x^b = x^(a-b). The power rule states (x^a)^b = x^(ab). Additional rules: x^0 = 1 (for x not 0), x^(-a) = 1/x^a, and (xy)^a = x^a * y^a. When simplifying expressions with exponents, apply these rules systematically. For example, (2x^3)^2 * 3x^(-1) = 4x^6 * 3x^(-1) = 12x^5. Always simplify coefficients and variable parts separately, then combine. Be careful with negative exponents and zero exponents, which are common sources of confusion.
How do you verify that a simplified expression is correct?
The most reliable verification method is numerical substitution: choose a specific value for each variable, evaluate both the original and simplified expressions, and confirm they produce the same result. Use non-trivial values (avoid 0 and 1 since they can mask errors). For example, to verify that (2x + 3)(x - 1) = 2x^2 + x - 3, substitute x = 5: original = (13)(4) = 52, simplified = 50 + 5 - 3 = 52. Test with at least two different values for extra confidence. For polynomial expressions, if two polynomials of degree n agree at n+1 or more points, they are identical. Graphing both expressions on a calculator and verifying they overlap is another excellent validation technique.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy