The FOIL Method and Multiplying Polynomials
Date: 05/25/2008 at 11:32:46 From: Mohamed Subject: multiplying using foil Multiply using foil (d-4)(d+3). How is it done?
Date: 05/25/2008 at 22:31:02 From: Doctor Peterson Subject: Re: multiplying using foil Hi, Mohamed. The FOIL idea is one way to apply the distributive property to multiply two binomials. Essentially what it means is that we need to multiply EACH term in the first factor by EACH term in the second. We can list them like this: first times first: d * d = d^2 [these are the First terms] first times second: d * 3 = 3d [these are the Outside terms] second times first: -4 * d = -4d [these are the Inside terms] second times second: -4 * 3 = -12 [these are the Last terms] You can diagram the four multiplications this way: ______ /___ \ / \ \ (d - 4)(d + 3) \_/ / \__/ The "outside" terms are the first and last; the "inside" terms are the two in the middle. Here is how I would actually write the work (including the step of combining like terms): (d - 4)(d + 3) = d^2 + 3d - 4d - 12 = d^2 - d - 12 Notice a couple important things I did: 1. Although some people memorize the method as First, Outside, Inside, Last, from which the method gets its name, you don't need to do so; all you really need is "each times each" and an orderly way to get to them all. Then it works for ANY two polynomials, not just binomials. 2. When a term is subtracted rather than added, just include the negative sign as part of the term, since "d - 4" is the same as "d + -4". That makes sure all the signs come out right. 3. In a typical problem like this one, you can expect the middle two terms to combine; be careful with the signs! When you have more than just binomials to multiply, a different way of writing it, shown in the following page, can give an easier way to organize your work: Explaining Algebra Concepts and FOIL http://mathforum.org/library/drmath/view/52844.html A sort of hybrid method, which still writes everything in a line but groups like terms naturally, looks like this for your example: (d - 4)(d + 3) = d^2 + 3d - 4d - 12 ------------- = d^2 - d - 12 If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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