Question 261851
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For a binomial times a binomial, use <b>FOIL</b>.  <b>FOIL</b> stands for <b>F</b>irst, <b>O</b>utside, <b>I</b>nside, <b>L</b>ast.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(x\,+\,3\right)\left(x\,+\,2\right)]


First:  *[tex \LARGE x\,\cdot\,x\ =\ x^2]  (the first terms of each)


Outside:  *[tex \LARGE x\,\cdot\,2\ =\ 2x]  (the first term of the first binomial and the last term of the second binomial)


Inside: *[tex \LARGE 3\,\cdot\,x\ =\ 3x]  (the last term of the first binomial and the first term of the second binomial)


Last: *[tex \LARGE 3\,\cdot\,2\ =\ 6]  (the last terms of each)


Add the terms:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 2x\ +\ 3x\ +\ 6]


Collect like terms:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 5x\ +\ 6]


There is nothing particularly sacred about the order in which the operations are performed.  It is just that Outside, Last, Inside, First = OLIF doesn't spell anything that a student would be likely to remember, and neither does FLIO, LFOI, etc.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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