1) The Difference of Cubes formula (which you should memorize now) is as follows:
. . . . .a<sup>3</sup> - b<sup>3</sup> = (a - b)(a<sup>2</sup> + ab + b<sup>2</sup>)
You should also know the Difference of Squares formula and the Sum of Cubes formula:
. . . . .a<sup>2</sup> - b<sup>2</sup> = (a - b)(a + b)
. . . . .a<sup>3</sup> + b<sup>3</sup> = (a + b)(a<sup>2</sup> - ab + b<sup>2</sup>)
2) What you have posted, "2 + 6i/3 - 4i", means the following:
. . . . .\(\displaystyle \L 2\,+ \,\frac{6i}{3}\, - \,4i\)
Is this what you meant? If so, then there isn't much simplifying to do: divide the 6 by the 3, and combine "like" terms. If not, then please reply with clarification. (You probably need to use grouping symbols.) Please also show what you have tried so far and clarify where you are stuck.
3) "Solve"? Or "evaluate"? I would suspect you are supposed to do the latter.
Using the Remainder Theorem to evaluate a polynomial at a given value of x is a fairly straight-forward matter of plugging the x-value into the synthetic-division algorithm. Where are you stuck in this process?
Thank you.
Eliz.
