Posted by Joel on September 23, 2002 at 18:28:52:
In Reply to: Difference of 2 Squares & Cubes posted by Rob on September 23, 2002 at 14:41:01:
: This is dumb and I Was hoping someone might be able to help me out here.
: Our Prof gave us this question, telling is there were 2 different answers to it. I can get one, that is easy. But I am stumped on the other.
: Here is is.
: Factor this as the difference of 2 Cubes & Squares.
: X^6 - Y^6
: He brokw it down this way
: (x^3)^2 - (y^3)^2 - this answer is below, I think.
: (X^2)^3 - (y^2)^3
: The Cubes answer is this
: (x-y) (x^2 + xy + y^2)
: (x+y) (x^2 - xy + y^2)
: Any help pointing me in the right direction would be helpful. I know it is probably right under my nose.
If you want to look at it as (x^3)^2 - (y^3)^2 first let x^3=A and y^3=B. That gives you:
A^2 - B^2 = (A - B)(A + B)
now substitute back to get (x^3-y^3)(x^3+y^3)
and now use your difference of cubes and sum of cubes formulas to further factor each of those terms.
Next, looking at it as (x^2)^3 - (y^2)^3 let x^2=A and y^2=B and start working with
A^3 - B^3 = (A-B)(A^2+AB+B^2)
and substitute back to get (x^2-y^2)*(x^4+x^2*y^2+y^4)
and now see what you can do to factor those some more.
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