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Common Algebra II Mistakes - Problem 2

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

A common mistake that Algebra 2 students make is whenever they are trying to expand x plus y² is to just distribute this squared sign in and to get x² plus y². To prove that this isn’t the case, we’re going to go to a more straight forward example. What we have here is3 plus 4, parenthesis squared.

We now have to use our parenthesis first so 3 plus 4 is 7, 7² is equal to 49. If we just distributed this squared sign in what we would end up with is 3² which is 9 plus 4² which is 16, 9 plus 16 is 25. Obviously 49 is not equal to 25 so we missed something when we distributed that square thing out. What we really have to do is FOIL.

This is the same thing as x plus y times x plus y and whenever we have a binomial times a binomial what we have to do is FOIL. So we do our first term, we get x², our outers and our inners we both get xy, so we end up with 2xy and plus y². I know it would be a lot easier if we could just distribute this 2 in and we wouldn’t have to deal with oiling but unfortunately it’s not the case. So whenever you see something plus something squared you really have to FOIL it out. You can’t just say x² plus y² or whatever your terms are squared.

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