# Thread: Simpify & product factoring problem..

1. ## Simpify & product factoring problem..

Perform the indicated operations and simplify. (note: special product (factoring) formulas)

( (8 x^3) / (x - 1) ) / ( (2 x^2) / (x^3 - 1) )

= ( (8x^3) / (x-1) ) * ( (x^3-1) / (2x^2) ) /* multiply by the reciprocal of the denominator

= ( (4x) / (x-1) ) * ( (x^3-1) ) /* Simplified

= ( (4x^4 - 4x) / (x-1) ) /* Product

okay, where does the solution go from there, assuming everything was done correctly up to that point?

the solution should be similar to: ___ x^3 + ___ x^2 + ___ x + ___

2. Originally Posted by snakeyesxlaw
Perform the indicated operations and simplify. (note: special product (factoring) formulas)

( (8 x^3) / (x - 1) ) / ( (2 x^2) / (x^3 - 1) )

= ( (8x^3) / (x-1) ) * ( (x^3-1) / (2x^2) ) /* multiply by the reciprocal of the denominator

= ( (4x) / (x-1) ) * ( (x^3-1) ) /* Simplified

= ( (4x^4 - 4x) / (x-1) ) /* Product

okay, where does the solution go from there, assuming everything was done correctly up to that point?

the solution should be similar to: ___ x^3 + ___ x^2 + ___ x + ___
note that, by the difference of two cubes formula, $\displaystyle x^3 - 1 = (x - 1)(x^2 + x + 1)$

apply that fact in the second to last line (or you could apply it in the last line after factoring out 4x from the numerator, but it's probably best to get it out of the way quickly)