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 Description  
 FOIL Pattern:  A method based on the Distributive Property that is often used to multiply two binomials.
The Distributive Property can be used to multiply two binomials. For example, (x + y)(b + c) means (x + y)b + (x + y)c because of the Distributive Property (look at the definition of distributive property and replace a with (x + y).) Then the Distributive Property can be used two more times to get xb + yb + xc + yc. FOIL, described in detail below, is just a way to remember the use of the Distributive Property in this situation. After you read about FOIL, try the procedure to multiply (x + y) and (b + c). Do you get the same result as given in this paragraph?

F means you multiply the first two terms together.
O means you multiply the outer terms together.
I means you multiply the inner terms together.
L means you multiply the last two terms together.


In (a + b)(c + d), a and c are the first terms since they appear first in each binomial. a and d are the outer terms since they are on the left and right sides, respectively. b and c are the inner terms since they appear in between the other two terms. b and d are the last terms since they appear second in each binomial.

Examples of FOIL

(3 + x)(2 - 3x) = 3*2 + 3*(- 3x) + x*2 + x*(- 3x) = 6 - 9x + 2x -. Combining like terms, we obtain: 6 - 7x - .

(x - 2)(1 - 5y) = x*1 + x*(- 5y) + (- 2)*1 + (- 2)*(- 5y) = x - 5xy - 2 + 10y. There are no like terms to combine.