Algebra (Does any one understand special factors)?
posted by Rae Rae .
I do not understand special factors, the teacher on Friday tried to explain in to me in class but she went so fast, and every time we complain that we don't understand it she gets mad. So could someone please help me with at least one problem so I can understand it better, and please explain it step by step.
Directions: Determine whether each trinomial is a perfect square trinomial. If so factor it.
1. x^216x+64

I think its a perfect square trionomial because you can square 4^2 to get 16 and 8^2 to get 64
(x  8)(x  8 ) 
first condition:
the first and last terms must be perfect squares, and they must both be positive
second condition:
the square root of the first term times the square root of the last term, then doubled, should be equal to the middle term.
e.g.
25x^2 + 60xy + 36y^2
square root of first: 5x
square root of last : 6y
product: 30xy
doubled: 60xy , so YES
e.g.
x^4  10x^2 + 25
square root of first: x^2
square root of last: 5
product : 5x^2
doubled : 10x^2, YES!
does that make sense?