Expert: Sherman D. - 9/14/2008

Question
Hey I'm in freshman in pre-calc and I've been working on this 100 problem worksheet and I'm down to my last three problems that I can't seem to get the right answer for.

They are:

1. Perform the operations and simplify.
(3 ^ -1/2 · 3x^5/2) /
((3x)^ 3/2),    x > 0

2.Multiply or find the special product.
[(x + 2) – y]2

3.Multiply or find the special product.
(3x + 5y)3

We're submitting it online and the system is really picky so I'm inputting something wrong somewhere in my answer but I'm not sure what. Your help is greatly appreciated!

Answer
1.)
(3x^(-1/2) * 3x^(5/2))/((3x)^(3/2))

(3^2 * x^((-1/2) + (5/2))) / (3^(3/2) * x^(3/2))

(3^2 * x^(4/2))/(3^(3/2) * x^(3/2))

3^(2 - (3/2)) * x^((4/2) - (3/2))

3^(1/2) * x^(1/2)

(3x)^(1/2)

----------------------------------

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

((x - 2) - y)((x - 2) - y)

(x - 2)^2 - (x - 2)y - (x - 2)y + y^2

((x - 2)(x - 2)) - 2(x - 2)y + y^2

(x^2 - 2x - 2x + 4) - 2xy + 4y + y^2

x^2 - 4x + 4 - 2xy + 4y + y^2

--------------------------------------

3.)
(3x + 5y)^3

(3x + 5y)(3x + 5y)(3x + 5y)

(9x^2 + 15xy + 15xy + 25y^2)(3x + 5y)

(9x^2 + 30xy + 25y^2)(3x + 5y)

27x^3 + 45x^2y + 90x^2y + 150xy^2 + 75xy^2 + 125y^3

37x^3 + 135x^2y + 225xy^2 + 125y^3

www.quickmath.com will expand this for you.