Multiplying Binomials

The Multiplying Binomials calculator computes the product of two linear binomial expressions in the form (ax + b)(cx + d) and returns the expanded quadratic polynomial along with each individual coefficient. The multiplication follows the distributive property, also known as the FOIL method (First, Outer, Inner, Last): multiply the first terms (a x c) to get the x^2 coefficient, the outer terms (a x d) and inner terms (b x c) and add them for the x coefficient, and multiply the last terms (b x d) for the constant term. The result is displayed as a fully expanded quadratic: acx^2 + (ad + bc)x + bd.

This tool is ideal for algebra students learning polynomial multiplication, teachers preparing classroom examples, tutors demonstrating the distributive property, and anyone who needs quick binomial expansion results for homework, test preparation, or self-study. It handles any real-number coefficients including integers, fractions (decimals), and negative values, making it suitable for problems ranging from basic algebra to advanced coursework. Unlike the FOIL calculator which shows each multiplication step individually, this calculator focuses on delivering the final expanded result and coefficient breakdown instantly.

Examples: (x + 2)(x + 3) = x^2 + 5x + 6 (x^2 coefficient: 1, x coefficient: 5, constant: 6). (2x - 1)(x + 4) = 2x^2 + 7x - 4 (x^2 coefficient: 2, x coefficient: 7, constant: -4). (3x + 2)(-x + 5) = -3x^2 + 13x + 10 (x^2 coefficient: -3, x coefficient: 13, constant: 10). (-x + 1)(x - 1) = -x^2 + 2x - 1 (x^2 coefficient: -1, x coefficient: 2, constant: -1).

How to use: Enter the four coefficients from your two binomials (ax + b)(cx + d) -- a and b from the first binomial, c and d from the second. Click Calculate and the expanded polynomial, x^2 coefficient, x coefficient, and constant term appear instantly. Use the Share button to copy a link with your current inputs for later reference or to share with classmates.