Help with 3 math questions?

Question

I am in pre calculus and this is just algebra review...

√= square root

1. Perform the indicated multiplication and simplify your answer if possible.

(2y + √3)(y√5 - 1)

I got 2y^2√5 - 2y + y√15 - √3

can i simplify any more?

For the next two equations: Assume that all exponents are non-negative integers and find the product..

2. (y^r + 1)(y^s - 4)

I got y^r+s - 4y^r + y^s - 4

3. (3y^2k + y^k +1)(y^k - 3)

I got 3y^2k+k - 9y^2k + y^k+k - 2y^k - 3

my question for this one is can the -9y^2k be added with the y^k+k because arent y^2k and y^k+k the same?

I just need my answers to be checked.

Thanks!

Answer 1

1) 2y^2√5 - 2y + y√15 - √3 and i don't see any way to simplify it so it seems right. i'm in Calculus 1 in college and i took a calculus course in high school so i should hope i'm doing this correctly.

2)y^r+s - 4y^r + y^s - 4   looks right yet again.

3) dang this is a long one. ah well, lets see...

    3y^(3k) - 9y^2k + y^2k - 3y^k + y^k - 3

    3y^(3k) - 8y^2k - 2y^k - 3

yes those two can be added together. and i think you forgot to multiply one term out in your problem. (y^k) * 3 so then you have 2 more terms to combine. what I did should be right. it's always a good idea to double check

Answer 2

that looks confusing

Answer 3

1) The solution is correct.

2) The solution is correct.

3) (3y^2k + y^k + 1)(y^k - 3)

3y^3k - 9y^2k + y^2k - 3y^k + y^k - 3

3y^3k -8y^2k -2y^k - 3

Good job!