|
Question 542491: what are the steps to solving a^2-b^2/a^3-b^3
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you start with:
(a^2 - b^2) / (a^3 - b^3)
you factor the numerator to get:
[(a-b)*(a+b)] / (a^3 - b^3)
you factor the denominator to get:
[(a-b)*(a+b)] / [(a-b)*(a^2+ab+b^2)]
the (a-b) in the numerator and the denominator cancel out and you are left with:
(a+b) / (a^2+ab+b^2)
since you can't factor (a^2+ab+b^2) any further, that's your answer.
you needed to know the special formulas involved.
those are:
(a^2 - b^2) = (a-b)(a+b)
(a^3-b^3) = (a-b)(a^2+ab+b^2)
they should be in your text.
they are also in the following lesson on factoring polynomials from wtamu.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut7_factor.htm
look for the section on "factoring a sum of two cubes" and "factoring a difference of two cubes".
the whole tutorial is worth a read.
|
|
|
| |
