How to Multiply Binomials Using Foil Method Easy

When multiplying two binomials you must use the distributive property to ensure that each term is multiplied by every other term. This can sometimes be a confusing process, as it is easy to lose track of which terms you have already multiplied together. You can use FOIL to multiply binomials using the distributive property in an organized way.^[1]By simply remembering the words in the acronym, this method will help you multiply binomials quickly.

1

Write the two binomials side-by-side in parentheses. This setup helps you easily keep track of operations when using the foil method.
2

Ensure you are multiplying two binomials. A binomial is an algebraic expression with two terms.^[2] The FOIL method does not work when multiplying trinomials, or a binomial by a trinomial.
3

Arrange the binomials by terms. Most algebra problems will already be arranged this way, but if not, make sure the first term in each expression contains the variable, and the second term in each expression contains the coefficient.

1

Multiply the first terms in each expression. The F in FOIL stands for "first."
2

Multiply the outside terms in each expression. The O in FOIL stands for "outside," or "outer." The outside terms are the first term of the first expression, and the last term of the second expression.
3

Multiply the inside terms in each expression. The I in FOIL stands for "inside," or "inner." The inner terms are the last term of the first expression, and the first term of the second expression.
4

Multiply the last terms in each expression. The L in FOIL stands for "last."
5

Write the new expression. To do this, write out the new terms you created during the FOIL process. You should have four new terms.
6

Simplify the expression. To do this, combine like terms. Usually you will have two terms with the $x$ variable that need to be combined.

Add New Question

Question

Does this work If I am multiplying binomials with different variables?

Yes, you can use the FOIL method if the binomials have different variables, such as x and y. In this case, after you complete the steps, you will not have any like terms to combine, so your final expression will have four terms. For example, (2x -7)(5y + 3) would simplify to 10xy + 6x -35y - 21.
Question

What determines where I put the addition and subtraction signs?

The sign of each term of the expansion is the product of the signs of the terms you multiplied to get it. Meaning if you're doing (y-4)(5-2n), the term corresponding to inner is (-4)(5) = -20 inheriting the negative sign from the - in -4, and the term corresponding to last is (-4)(-2n) = +8n because both terms are negative and the product of two negatives is positive.
Question

How do I solve (x - 4)(x + 2) = 3(x - 1)?

(x - 4)(x + 2) = x² - 2x - 8. 3(x - 1) = 3x - 3. Therefore x² - 2x - 8 = 3x - 3. Then x² - 5 = 5x, and x² - 5x - 5 = 0. The left side of that equation cannot be factored, so you'd have to use the quadratic formula to solve for x. Thus, x = {5 +/- √[25 - (4)(1)(-5)]} ÷ (2)(1) = {5 +/- �√[25 + 20]} ÷ 2 = (5 +/- √45) ÷ 2 = (5 +/- 6.7) ÷ 2 = 5.85 or -0.85 (two values for x, which is normal with quadratic equations).