The acronym FOIL is a loose representation on how to multiply binomials, trinomials, and polynomials. FOIL stands for "First, Outer, Inner, Last", and each part represents a part in a multiplication of polynomials.For example, let's multiply these two binomials.(x + 3)(x - 7)An easy way to FOIL this and other such multiplications is to take each term in the first binomial and multiply them with each term in the other binomial. Multiply the first term in the first binomial with the first and second term in the second binomial, and then multiply the second term in the first binomial with the first and second term in the second binomial.After you multiply all the terms together, you add each separate product and simplify the resulting polynomial.As for the example...(x + 3)(x - 7)(First, Outer) a. x * x = x^2(First, Inner) b. x * (-7) = -7x(Inner, Inner) c. 3 * x = 3x(Inner, Outer) d. 3 * (-7) = -21(Add it all up) e. x^2 - 7x + 3x - 21 = x^2 - 4x - 21