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Factoring: Special Cases Part I - Problem 2
All right I’m a Math teacher and I’m going to let you in a little secret. When we have those Math teacher training days what they do is that they tell us how to torture students and one of the things they tell us to do is to give Geometry problems to students who are only in Algebra class kind of like this.
If the area of a square is 49m² plus 28m plus 4 find the side length. Okay so I know you guys aren't officially in a Geometry class but you can still do these problems because you know a lot about squares. You know that if you have a square all of the sides are equal length.
So if I were to call this s for side length all of those guys will be s for side length. You also know the way to find the area is to take your side and well just take your length and multiply it by width or for a square you are going to do side length times itself is equal to the area.
So what I’m looking for in this problem is some side length I don't know what it is squared is going to be equal to my area statement 49m² plus 28m plus 4. Something I don't know what it is yet, whatever goes in there times itself gives me this result. Okay so now I want to think about what I know about this statement a binomial squared gives me a perfect square trinomial that's what this is called. This statement right here represents a+bx itself and then we saw that the formula for a perfect square trinomial looks like this.
So what I need to do is translate this thing that has all just letters into this thing that has numbers also. But let's look out at 49m² that is my a value times itself. Well if 49m² is the square of something than a that has t be 7m because a squared will give me 49m squared.
7m will is my first part of my side length I think. Then let's look at this last piece, this last term represents b² so b has to be 2. I think my side length is 7m plus 2 I’m going to double check by Foiling and make sure I didn't make any errors in my definition of a perfect square trinomials let's just double check.
I think 7m plus 2 times itself remember the area of a square is side length times itself I think is equal to this let's just check, Foil; first, outers, inners, last. 49m² plus 14m plus 14m again plus 4. Good if I combine those middle terms I do get my original area statement.
That's how I know I did it correctly so this is the side of my square even though I’m not in the Geometry class I could still do this problem based on what I do know about squares I know their area is equal to the side length times itself.