FOIL Method

Multiplying BinomialsYe Olde FOIL Method

Welcome to the Verde Learning Center Tutorial on the Foil Method for Multiplying Binomials 1Arrg - Whats a binomial?A binomial is a algebraic expression that has 2 termsEach term will contain numbers and or variables(letters)The terms are separated by addition or subtraction signsX + 7is a binomialHere are some other binomial examples

FOIL Method Multiplying Binomials3 + yx - y2x + 110 + 1

Whats a binomial? A binomial is an algebraic expression that has 2 terms. Each term will contain numbers and or variables (which are letters). The terms are separated by addition or subtraction signs. X + 7 is a binomial.2What not to do - A common mistake Students frequently try to multiply only the first and last terms of the binomial. This is only part of the answer.

Foil Method Multiplying Binomials(a + b)(a + b)= a2 + b2

Heres a common mistake. 3A common mistake

FOIL Method Multiplying Binomials(10 + 1)(10 + 1)= 102 + 12(10 + 1)(10 + 1)= (11) (11) = 121= 100 + 1 = 101Since we know that 10+1 is 11 and 11 times 11 is 121 we can see that something is wrong with this method

Lets substitute numbers and check. Only multiply the first and last terms gives us a result of 101. However 10+1 is 11 and 11 x 11 is 121 so we can see there is something wrong with this method4Time to break out the Mystery FOILFOIL Method Multiplying Binomials

Time to break out the mystery foil.

5FOIL Method Multiplying Binomials(10 + 1)(10 + 1)(10 + 1)(10 + 1)= (11) (11) = 121= 10FOIL stands for

FirstOutsideLastInside*10+++10***111011= 100+ 10+ 10+ 1= 121This is a great method for multiplying binomials

FOIL stands for First Outside Inside and Last We will multiply the first terms of each binomial, then the terms on the outside, then the inside terms, and finally the last terms. This results in 121 which is the correct answer. Foil is a great method for multiplying binomials.

6FOIL Method Multiplying Binomials(x + 3)(x + 4)= xYe other example:

FirstOutsideLastInside*x+++x***43x34= x2+ 4x+ 3x+ 12 + 7x= x2 + 7x +12 Combine the like terms.

7FOIL Method Multiplying Binomials(x + y)(x + y)= xHeres the please show me another example:

FirstOutsideLastInside*x+++x***yxyyy= x2+ xy+ xy+ y2+ 2xy = x2 + 2xy + y2 Combine the like terms.

Here is another example. We will multiply x +y and x+y. when we multiply the first terms we have x*x when we multiply the outside terms we have x*y when we multiply the inside terms we have x*y and the last terms result in y*ySimplifying we have x squared plus xy plus xy plus y squaredCombining the like terms we have x squared plus 2xy plus y squared

8FOIL Method Multiplying Binomials(x + 2)(x - 3)= xAnother olde example:

FirstOutsideLastInside*x+++x***-32x2-3= x2+ -3x+ 2x+ -6-x = x2 -x -6Dont forget the negative sign!

Here is last example. When there is subtraction in a binomial, we treat the subtraction sign as if it were attached to the number so in the binomial x 3 we will have an x term and a negative 3 term.

In this example, we will multiply x +2 and x-3. multiplying the first terms we have x*x when we multiply the outside terms we have x*-3 when we multiply the inside terms we have 2*x and the last terms result in 2*-3Simplifying we have x squared plus -3x plus 2x plus -6Combining the like terms we have x squared plus -x plus -6Adding a negative number is the same as subtract that number so we further simplify and writeX squared minus x minus 6

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