How to Multiply Binomials
Binomials are widely used in the field of algebra, as well as in the physical and chemical sciences. Binomials are alegbraic expressions that contain two monomials and are also considered very basic polynomials. Monomials are expressions that may contain one or more of the following: a base, a variable (denoted by a letter) and an exponent. While seeming complex, multiplying two binomials together is fairly easy if you are familiar with a few rules. The FOIL rule is the most common rule to use when multiplying two binomials together. It stands for First, Outer, Inner, Last and represents the order in which you should multiply the terms of the two binomials.
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Instructions
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1
Multiply the first term of the first binomial with the first term of the second binomial, remembering that when multiplying the values to multiply the bases and add the exponents. For instance, in the example (2a + 3b)(a + 7b) you would multiply 2a * 1a to get 2a^2.
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2
Multiply the first term of the first binomial with the second term of the second binomial (the "outer" numbers). In the example (2a + 3b)(a + 7b) you would multiply 2a * 7b. This term simplified equals 14ab.
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3
Multiply the second term of the first binomial with the first term of the second binomial (the "inner" numbers). In the example (2a + 3b)(a + 7b) you would multiply 3b * 1a. This term simplified equals 3ba, or 3ab.
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4
Multiply the second term of the first binomial with the second term in the second binomial (the "last" numbers). In the example (2a + 3b)(a + 7b) you would multiply 3b * 7b, which equals 21b^2.
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Put all four values into a single equation, adding them together. In the example (2a + 3b)(a + 7b), you have the terms 2a^2, 14ab, 3ab, and 21b^2. Because 14ab and 3ab have similar letters, these can be added together to simplify. The answer to the example, therefore, is 2a^2 + 17ab + 21b^2.
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