About the FOIL calculator
This free FOIL calculator multiplies two binomials in the form (ax + b)(cx + d) and shows the result as a single polynomial. FOIL stands for First, Outer, Inner, and Last: you multiply the first terms (a and c), then the outer terms (a and d), then the inner terms (b and c), then the last terms (b and d). Adding those four products gives the expanded form acx² + (ad + bc)x + bd. You enter a, b, c, and d (and optionally change the variable letter from x), click Get result, and the calculator displays the two binomials, each FOIL step, and the final polynomial. No sign-up or download is required; the tool is mobile-friendly and works in your browser.
The FOIL method is taught in algebra courses because it gives a clear, repeatable order for expanding (ax + b)(cx + d). It is equivalent to applying the distributive property twice: (ax + b)(cx + d) = ax(cx + d) + b(cx + d), then expanding each part. FOIL is especially useful when learning to factor quadratics, solve equations, and graph parabolas. Engineers and scientists often use binomial multiplication in formulas; this calculator helps you check your work or explore different coefficients quickly. You can use whole numbers, decimals, or negative values for a, b, c, and d.
Common examples include (x + 2)(x + 3) = x² + 5x + 6 and (x − 1)(x + 4) = x² + 3x − 4. For the first, enter a=1, b=2, c=1, d=3; for the second, a=1, b=−1, c=1, d=4. The calculator shows the four FOIL products and combines like terms to give the final answer. Knowing FOIL also helps on standardized tests when you need to expand (x + a)(x + b) quickly: the result is x² + (a + b)x + ab. Use this FOIL calculator for homework, quizzes, or any time you need to multiply two binomials and see the steps clearly.
This FOIL method calculator is free, responsive on phones and tablets, and shows every step so you can learn the method or verify your algebra. For solving quadratic equations or factoring, pair it with our quadratic formula or factorization calculators. The page is dedicated to expanding (ax + b)(cx + d) using the First, Outer, Inner, Last rule.