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This algebra 1 math tutorial from NutshellMath offers homework help in basic operations involving polynomials. Polynomials are algebraic expressions assembled out of multiple terms using only addition, subtraction, multiplication and whole-number exponents. Polynomials are one of the most important subsets of all algebraic expressions.


In this tutorial, the teacher introduces the FOIL method for multiplying two binomials, or polynomials consisting of only two terms. The FOIL method is an application of the distributive property, meant to remind the student how to distribute one set of terms over another.

FOIL stands for First, Outer, Inner, Last. The "first" terms are first terms in each of the two binomials. These terms are multiplied together and added to the next product. The next product is that of the "outer" terms, or the first term of the first binomial and second term of the second binomial. The sum of the "first" and "outer" is added to the product of the "inner" terms, or the second term of the first binomial and first term of the second binomial. The last product added to the sum of the other three is that of the "last" terms, or the product of second term of the first binomial and the second term of the second binomial. When adding together products using the FOIL method, it is very important to pay attention to the sign of the products.

The FOIL method is the most useful method for remembering how to find the product of two binomials. The examples in this tutorial demonstrate how to use the FOIL method effectively.