FOILing and Explanation for FOIL – Practice Problems

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One way of getting the product of two binomials is the FOIL method. The term “FOIL” represents the position of the terms of the binomials; i.e. It is an acronym for “First-Outer-Inner-Last”.

Using the FOIL method means performing the following steps:
1. Take the product of each pair of terms of the binomials - the first, outer, inner, and last terms.
2. Simplify the product by combining existing like terms.
3. Arrange the terms of the product in descending order according to their degree.

More specifically, if we want to multiply two binomials, like (a+b) and (c+d), then we multiply the first terms of each binomial, a*c, then we multiple the outer two terms, a*d, then the inner two terms, b*c, and finally the last two terms, b*d. Then we add these products together to get that

(a+b)(c+d)=a*c+a*d+b*c+b*d,

making sure that we simplify by combining like terms, and rearrange terms from highest to lowest degree (by convention).

The FOIL method is an essential tool, as it is needed in any instance involving multiplying polynomials.

Perform arithmetic operations on polynomials.

CCSS.MATH.CONTENT.HSA.APR.A.1

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Exercises in this Practice Problem
Calculate $(25 + 2x)(20 + x)$ using the FOIL method.
Determine the area of the zoo via the distributive property and the FOIL method.
Identify the right formula for calculating the area.
Calculate the new area of the zoo.
Decide when the FOIL method can be used.
Find the mistakes in the calculations.