FOIL Calculator

FOIL is a mnemonic for multiplying two binomials. Its letters stand for First, Outer, Inner, and Last, the four pairs of terms created by the distributive property. For the product (ax + b)(cx + d), the first terms produce ac times x squared, the outer terms produce ad times x, the inner terms produce bc times x, and the last terms produce bd. Adding the two middle products gives the standard quadratic form ac times x squared plus (ad + bc) times x plus bd. This calculator accepts linear binomials written with x, a numerical coefficient, and a signed constant. Inputs such as 2x + 3, x - 5, -x + 4, and 0.5x - 2 are supported. When no coefficient is written before x, the coefficient is understood to be 1; when only a minus sign appears, it is understood to be -1. The output omits unnecessary coefficients of 1 and formats positive and negative terms with familiar algebraic signs. The FOIL method is not a separate algebraic law. It is simply a memorable way to apply distribution to exactly two binomials. Every term in the first factor must multiply every term in the second factor. Once those four products are written, like x terms are combined. The squared term and constant term generally cannot combine with anything else because their powers differ. For example, expanding (2x + 3)(3x + 4) gives first product 6x squared, outer product 8x, inner product 9x, and last product 12. Combining 8x and 9x yields 17x, so the final polynomial is 6x squared + 17x + 12. A useful verification is to substitute a simple value such as x equal to 1 into both the original product and expanded polynomial; both forms should produce the same number. FOIL is especially useful when learning polynomial multiplication, solving quadratic equations, checking factorizations, and simplifying algebraic expressions. For products with more than two terms in either factor, use the full distributive method instead: multiply every term in one polynomial by every term in the other. The same principle applies, but the four-letter mnemonic no longer covers all required products.