Simplyfying (2x^2 - y)^2, (3y - 1)^3, etc.

[kpx001]

Hi, Am i doing these problems correctly? I cant determine when to stop.
Problems: 1-7

1. (2x^2 - y)^2

. . .(2x^2 - y) (2x^2 - y)

. . .4x^4 - 4x^2y + y^2

2. (3y - 1)^3

. . .(3y - 1)(3y - 1)(3y - 1)

. . .(9y^2 - 6y)(3y - 1)

. . .27y^3 - 27y^2 - 6y

. . .3y(9y^2 - 9y - 2)

3. (x^2 - 2x - 3) / (2x^2 + 5x + 3)

. . .(x - 3)(x + 1) / (2x - 1)(x + 3)

4. x^3/(x - 1) x (x^3 - 1)/x^2

I forgot what to do for this problem.

 

[stapel]

1) Correct.

2) Since the last term in the expansion will, necessarily, be the cube of the 1, the constant term must be 1, not 6 or 6y.

Hint: Check your multiplication. (3y - 1)(3y - 1) cannot be 9y² - 6y.

. . . . .(3y - 1)(3y - 1) = (3y)(3y) + (-1)(3y) + (3y)(-1) + (-1)(-1) = ...?

3) Are you supposed to factor and see if it can be simplified, or are you supposed to do long division? And are the signs on the terms correct? (Usually, for factoring, they like to have one of the factors cancel, and that would happen, if some of the signs were different.)

4) Where does the middle "x" go? What were the instructions?

Thank you.

Eliz.