How to use the polynomial expansion calculator
Expanding a product such as (2x² + 3x − 1)(x − 4) by hand means multiplying every pair of terms and then collecting like degrees, which is where mistakes creep in. Enter the two polynomials here and the tool expands the product and writes it in descending standard form. Type coefficients and powers together, as in 2x^2+3x-1; the multiplication sign may be left out.
Internally each input becomes an array of coefficients indexed by degree, and the two arrays are multiplied by convolution. A term of degree i times a term of degree j lands in degree i+j, so the product of the two coefficients is added into that slot. Terms may be typed in any order, and repeating a degree simply adds the coefficients together. Each polynomial is supported up to degree 10.
The results show P(x) and Q(x) in standard form, the expanded product, its degree, the number of nonzero terms, and a table of coefficients by degree. The final check row substitutes x = 2 and compares P(2) × Q(2) with R(2), so you can confirm the expansion at a glance. No thousands separators are used inside the expressions. Inputs with parentheses, several different variables, or functions such as sin and log are not supported.
Frequently Asked Questions
Write coefficients and powers together, such as 2x^2+3x-1. The multiplication sign may be omitted, and parentheses or functions like sin and log are not supported.
Both polynomials are turned into coefficient arrays and multiplied by convolution, adding every pair of like degrees. The order in which you type the terms does not matter.
Yes. The check row substitutes x = 2. If P(2) × Q(2) equals R(2) for the expanded polynomial, the expansion is correct.