SOLUTION: How would I use the FOIL system

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Question 134867This question is from textbook Glencoe Algebra 2
: How would I use the FOIL system This question is from textbook Glencoe Algebra 2

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
FOIL stands for First, Outside, Inside, Last. Used when multiplying two binomials.

For example: %28x%2B2%29%28x-1%29

The x in the first binomial and the x in the second binomial are FIRST: %28green%28x%29%2B2%29%28green%28x%29-1%29

The x in the first binomial and the -1 in the second are OUTSIDE: %28green%28x%29%2B2%29%28x-green%281%29%29

The +2 in the first binomial and the x in the second are INSIDE: %28x%2Bgreen%282%29%29%28green%28x%29-1%29


The +2 in the first binomial and the -1 in the second are LAST: %28x%2Bgreen%282%29%29%28x-green%281%29%29

Multiply the FIRSTs: x%2Ax=x%5E2

Multiply the OUTSIDEs: x%2A-1=-x

Multiply the INSIDEs: 2%2Ax=2x

Multiply the LASTs: 2%2A-1=-2

Add the four products: x%5E2-x%2B2x-2

Collect like terms: x%5E2%2Bx-2

So: %28x%2B2%29%28x-1%29=x%5E2%2Bx-2

You really don't have to do multiplication of binomials in any particular order, but FOIL gives you a systematic approach that ensures that you don't either forget one of the products or duplicate any of the products. Besides, LIOF doesn't spell anything.

Hope that helps,
John