Hi I am taking my final right now and I have a few problems I am stuck with, can you help me?
1. (x-3y)(x squared+3xy+9y squared)
2. (x+2)(x-2)(x-3)
they both need to be multiplied
thanks
I will critique your thinking, if you post it. This is your final...
it makes no sense! want in the world!
Of course, I can help you with those problems! Let's start by expanding the expressions.
1. To expand the expression (x - 3y)(x^2 + 3xy + 9y^2), we'll use the distributive property. We'll multiply each term in the first expression (x - 3y) by each term in the second expression (x^2 + 3xy + 9y^2).
(x - 3y)(x^2 + 3xy + 9y^2) = x(x^2 + 3xy + 9y^2) - 3y(x^2 + 3xy + 9y^2)
Now, we can multiply each term separately:
x * x^2 + x * 3xy + x * 9y^2 - 3y * x^2 - 3y * 3xy - 3y * 9y^2
Simplifying each term:
x^3 + 3x^2y + 9xy^2 - 3x^2y - 9xy^2 - 27y^3
Combining like terms:
x^3 - 3x^2y - 9xy^2 - 27y^3
So, the expanded form of (x - 3y)(x^2 + 3xy + 9y^2) is x^3 - 3x^2y - 9xy^2 - 27y^3.
2. To expand the expression (x+2)(x-2)(x-3), we can proceed by multiplying each pair of factors at a time using the distributive property.
First, let's multiply (x + 2) and (x - 2):
(x + 2)(x - 2) = x * x + x * (-2) + 2 * x + 2 * (-2)
Simplifying each term:
x^2 - 2x + 2x - 4
Combining like terms:
x^2 - 4
Now, we need to multiply the result by (x - 3):
(x^2 - 4)(x - 3) = x^2 * (x - 3) - 4 * (x - 3)
Simplifying each term:
x^3 - 3x^2 - 4x + 12
So, the expanded form of (x + 2)(x - 2)(x - 3) is x^3 - 3x^2 - 4x + 12.
I hope this helps you with your final exam! If you have any further questions, feel free to ask.