SOLUTION: how do i find the product? (x-1) (x+3) (x-3) (x^3) - x^2 (3)(3x) = x^3 -2x + 9 ?? (my best guess)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: how do i find the product? (x-1) (x+3) (x-3) (x^3) - x^2 (3)(3x) = x^3 -2x + 9 ?? (my best guess)       Log On


   



Question 404630: how do i find the product? (x-1) (x+3) (x-3)
(x^3) - x^2 (3)(3x) = x^3 -2x + 9 ??
(my best guess)

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
(x-1) (x+3) (x-3)
It will require two stages to multiply this out:
  1. Multiply two of these three factors. (And since multiplication is Commutative and Associative we can pick any two factors to multiply to start!)
  2. Multiply the answer from step 1 by the remaining factor.

Since we get to pick which pair of factors to multiply I am going to pick the easiest pair. The last two factors, (x+3) and (x-3), fit the pattern for %28a%2Bb%29%28a-b%29+=+a%5E2-b%5E2. So multiplying them will be easy. Using the pattern, with "a" being x and "b" being 3 we get:
%28x-1%29+%28%28x%29%5E2+-+%283%29%5E2%29
or
%28x-1%29+%28x%5E2+-+9%29
Now we multiply what is left. There is no pattern for this. Since it is one binmial times another we can use FOIL. But before that I like to rewrite the subtractions as additions. Subtractions are a common source of confusion and errors.
%28x%2B+%28-1%29%29+%28x%5E2+%2B+%28-9%29%29
Now we'll use FOIL:
x%2Ax%5E2+%2B+x%2A%28-9%29+%2B+%28-1%29%2Ax%5E2+%2B+%28-1%29%28-9%29
which simplifies as follows:
x%5E3+%2B+%28-9x%29+%2B+%28-x%5E2%29+%2B+9
Usually terms are put in descending order of the exponents so this would become:
x%5E3+%2B+%28-x%5E2%29+%2B+%28-9x%29+%2B+9