Equivalent Expression Calculator
Enter an algebraic expression and get equivalent forms: simplified, expanded, and factored. Includes step-by-step analysis and sample evaluations.
Enter an algebraic expression using x as the variable. Use ^ for exponents.
What are equivalent algebraic expressions?
Equivalent algebraic expressions are different forms of the same mathematical expression that produce the same result for any value of the variable. For example, 2(x + 3) and 2x + 6 are equivalent because they give the same answer for any value of x. Simplifying, expanding, and factoring all produce equivalent expressions.
How do I simplify an algebraic expression?
To simplify: (1) Remove parentheses by distributing, (2) Combine like terms (terms with the same variable and exponent), (3) Simplify any fractions. For example: 3x + 2(x - 4) + 5 = 3x + 2x - 8 + 5 = 5x - 3.
How do I expand a factored expression?
To expand, use the distributive property: multiply each term inside the parentheses by the term outside. For binomials, use FOIL (First, Outer, Inner, Last). Example: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6.
How do I factor an algebraic expression?
To factor: (1) Find the greatest common factor (GCF) of all terms, (2) Write the GCF outside parentheses, (3) Inside parentheses, write what remains when each term is divided by the GCF. Example: 6x² + 9x = 3x(2x + 3). For trinomials, find two numbers that multiply to give ac and add to give b.