Overview
This interactive calculator expands and simplifies polynomial expressions in \(x\). It applies the distributive property to remove parentheses and combines like terms to produce the fully simplified result. It's a useful tool for checking your work while adding, subtracting, and simplifying polynomials.
Interactive Expansion Calculator
Enter your expression using +, -, *, ^, and parentheses.
Example: 3*(x-2)-2(x-1)*(x-4).
Example — Expand and Simplify \(2(x - 4) - 3(x + 4)\)
Step-by-Step Solution
Step 1 — Expand each product:
\[ 2(x - 4) - 3(x + 4) = 2x - 8 - 3x - 12 \]Step 2 — Group like terms:
\[ = (2x - 3x) + (-8 - 12) \]Step 3 — Combine:
\[ = -x - 20 \]Final answer: \( 2(x - 4) - 3(x + 4) = -x - 20 \).
Syntax Examples
Copy any of the following into the calculator and click Expand and Simplify:
-2*(x-2) + 44*(x-2) - 3*(x+5)(x-2)*(x+5) - 3*(x+5)(x-2)^2 + 4*(x+5)-(x-2)*(x+7) + 2(x+3)*(x+1)2*(x-2)^3 - (x-2)^22*(x-2)*(x-3)*(x+4)
Common Input Errors
- Missing multiplication sign — write
2*x, not2x, when a number multiplies a variable. (Coefficients like2(x+1)are OK.) - Unmatched parentheses — every
(needs a matching). - Wrong variable — the calculator is built for polynomials in
x. Expressions iny,t, or other variables will not expand correctly. - Unsupported functions — this calculator handles polynomials only. It does not handle square roots, logarithms, or trigonometric functions.
Frequently Asked Questions
How do you expand and simplify a polynomial?
Apply the distributive property to remove parentheses — multiply each outside term by each inside term. Then combine like terms (same variable and same power). For example, \(2(x - 4) - 3(x + 4) = 2x - 8 - 3x - 12 = -x - 20\).
What syntax does the calculator accept?
Use +, -, *, ^, and parentheses. The variable must be x. Example: 3*(x-2)-2(x-1)*(x-4).
Why does my expression show an error?
Common causes: unmatched parentheses, a variable other than x, or a missing * between a coefficient and a variable (e.g., 2x should be 2*x).
What is a polynomial?
A polynomial is an expression built from terms of the form \( ax^n \) where \( n \) is a non-negative integer. Examples: \( 3x^2 - 5x + 2 \), \( x^5 - 1 \), and \( 7 \). Expressions with \( x \) in a denominator or under a square root are not polynomials.
More References and Links
Last updated: October 17, 2026