# Math Help - Factoring and Simplifying Expressions.

1. ## Factoring and Simplifying Expressions.

This is a for a take home test. I have completed enough problems to pass this test, but the more questions I get the higher my grade is. So, if you can help me with a question or two that would be of great help to me.

The first question I need help states : Factor Completely

(b+3)^3 -27

I know I can make -27 into -3^3, but this expression is still not factored completely and the teacher will subtract a few points for that!

The second question states : Factor Completely

6y^2 (y^2+3)^3 (y^3 +5) + 6y (y^3+5)^2 (y^2 +3)^2
I know that there are common factors here. I could get partial credit in this problem. I don't know how to rearrange the factors though.

The third question states : Factor Completely
x^4m -1
I will check this one after I finish typing this message.

The fourth question states: Simplify the expressions.

x^-1 -4Y / (x^-1 -2y) (X^-1 +2y)
This one is the one I need the most help.

The fifth question states: Simplify the expressions.

x-1 + 2/x-4 and this is all over / x+3 + 6/x-4.

I got a common denominator using the LCD however I am unsure of how to proceed after. I will get partial credit but I am unsure on how to finish it off. Hopefully I get it, if not it's okay.

The final question states: A comical funnel has a height of h of 4 inches and a lateral surfaces area L of 15pi square inches. Find the radius 2 of the cone. My brother tried to help me with this problem and we are working on it.

If you can help me with a problem or two, that would be great and boost my grade. It would help me tremendously and could be the difference between getting a B for the quarter and an A. I need this by Monday. If you can help thanks.

2. Hi there DenisNY100, welcome to MHF!

Originally Posted by DenisNY100

The first question I need help states : Factor Completely

(b+3)^3 -27

I know I can make -27 into -3^3, but this expression is still not factored completely and the teacher will subtract a few points for that!
You have started this question in the right manner. Now expand on the idea using the rule

$x^3-y^3 = (x-y)(x^2+xy+y^3)$

Have a go.. $(b+3)^3 -27 = (b+3)^3 -3^3$

In your case $x = b+3$ and $y = 3$