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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] X Research source }By simply remembering the words in the acronym, this method will help you multiply binomials quickly.
Steps
Part 1
Part 1 of 2:Setting Up the Problem

1Write the two binomials sidebyside in parentheses. This setup helps you easily keep track of operations when using the foil method.
 For example, if you are multiplying and , you would set up the problem like this:
 For example, if you are multiplying and , you would set up the problem like this:

2Ensure you are multiplying two binomials. A binomial is an algebraic expression with two terms.^{[2] X Research source } The FOIL method does not work when multiplying trinomials, or a binomial by a trinomial.
 A term is a single number or variable, such as or , or it could be a multiplied number and variable, such as .^{[3] X Research source }
 Read Multiply Polynomials for instructions on multiplying other types of polynomials.
 For example, you could NOT multiply using the FOIL method, because the second expression is a trinomial, with three terms.
 You could multiply , because both expressions are binomials, with two terms each.

3Arrange 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.
 Setting up the problem this way makes simplifying easier.
 A coefficient is a number without a variable.
 For example, you would change to .
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Part 2
Part 2 of 2:Multiplying Binomials

1Multiply the first terms in each expression. The F in FOIL stands for “first.”
 Remember when multiplying a variable by itself, such as , the result is a squared variable ().
 For example, if your problem is , you would first calculate:

2Multiply 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.
 Pay close attention to addition and subtraction. If the second binomial is a subtraction expression, that means in this step you will be multiplying a negative number.
 For example, for the problem , you would next calculate:

3Multiply 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.
 Pay close attention to addition and subtraction. If the first binomial is a subtraction expressions, that means in this step you will be multiplying a negative number.
 For example, for the problem , you would next calculate:

4Multiply the last terms in each expression. The L in FOIL stands for “last.”
 Pay close attention to addition and subtraction. If either binomial is a subtraction expression, that means in this step you will be multiplying a negative number.
 For example, for the problem , you would next calculate:

5Write the new expression. To do this, write out the new terms you created during the FOIL process. You should have four new terms.
 For example, after multiplying , your new expression is .

6Simplify the expression. To do this, combine like terms. Usually you will have two terms with the variable that need to be combined.
 Pay close attention to positive and negative signs as you add or subtract.
 For example, if your expression is , you would simplify by combining . Thus, the expression simplifies to
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Community Q&A

QuestionDoes this work If I am multiplying binomials with different variables?Community AnswerYes, 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.

QuestionWhat determines where I put the addition and subtraction signs?Community AnswerThe 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 (y4)(52n), 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.

QuestionHow do I solve (x  4)(x + 2) = 3(x  1)?DonaganTop Answerer(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).

QuestionJohn goes on a diet and loses one ninth of his weight, n. What is his weight after going on a diet?DonaganTop AnswererIf he loses oneninth of this weight, that means his new weight is 8/9 of his original weight. So his new weight is (8n/9).
Video
Tips
 You can think of this as two separate distributions: (2x)(5x + 3) added with (7)(5x + 3)Thanks!
Things You'll Need
 Paper
 Pencil or pen
 To know how to multiply, add, and subtract
References
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Reader Success Stories

"I had forgotten what FOIL was, so I had to go through the steps."