refresher algebra that just isin't clicking

[mtrouse]

6x^2 + 12x        .   x^3 + 64
3x^2 +14x +8        4x^2-49

=   6x(x+2)
  (3x+2)(x+4)       (2x+7)(2x-7)

This is all I can get. I can not figure out the cube root of 64, well I know it is 4 but can't figure out how to solve the equation. Not sure if I did the rest right either.

Thank you!!!!!

 

[Denis]

Please repost CLEARLY:

6x^2 + 12x . x^3 + 64 : what does the dot mean?

3x^2 +14x +8 4x^2-49 : is that 2 different equations?

And WHAT is the question? Simplify? Solve for x?

 

[stapel]

From the little dot in what you posted, I'm going to guess that the topic is "multiplying rational expressions", that the instructions were to "simplify the following product", and that the exercise is the following:

. . . . .\(\displaystyle \L \left( \frac{6x^2\, +\, 12x}{3x^2\, +\, 14x\, +\, 8}\right)\, \left(\frac{x^3\, +\, 64}{4x^2\, -\, 49}\right)\)

With respect to factoring x³ + 64, you'll want to memorize the formulas for factoring sums and differences of cubes:

. . . . .\(\displaystyle \L a^3\, -\, b^3\, =\, (a\, -\, b)(a^2\, +\, ab\, +\, b^2)\)

. . . . .\(\displaystyle \L a^3\, +\, b^3\, =\, (a\, +\, b)(a^2\, -\, ab\, +\, b^2)\)

Please reply with corrections, if I have mistaken your meaning. Thank you.

Eliz.

 

[mtrouse]

Thank you!!!!