# Algebra problem

• Apr 22nd 2011, 08:22 AM
stripe501
Algebra problem
I had an assignment recently where I had to derive the formula for the volume of a fulcrum. While simplifying i found that an expression (a^3-b^3)*(c/a-b) will evaluate to (a^2+ab+b^2) but I do not understand how, could someone please explain how this expands?
• Apr 22nd 2011, 08:31 AM
emakarov
I don't see how (a^3-b^3)*(c/a-b) can simplify to (a^2+ab+b^2). One reason is that the first expression contains c, but the second one does not. On the other hand, (a^3-b^3)*c/(a-b) simplifies to (a^2+ab+b^2)*c, which can be checked by multiplying (a^2+ab+b^2) and (a-b).
• Apr 22nd 2011, 08:36 AM
stripe501
Yeah I meant (a^2+ab+b^2)c and I have checked on my calculator but i would just like someone to explain how that works out
• Apr 22nd 2011, 09:02 AM
emakarov
Do you need explanation how to multiply (a^2+ab+b^2) and (a-b)? Use the distributivity law: multiply each term from the first factor by each term of the second factor and add all of the results together.
• Apr 22nd 2011, 09:08 AM
stripe501
I would like someone to explain how(a^3-b^3)*(c/a-b) evaluates to c*(a^2+ab+b^2)
• Apr 22nd 2011, 09:35 AM
Wilmer
Quote:

Originally Posted by stripe501
I would like someone to explain how(a^3-b^3)*(c/a-b) evaluates to c*(a^2+ab+b^2)

You were already told that a^3 - b^3 = (a^2 + ab + b^2) * (a - b) ; so simply cancel out the (a - b) terms.
• Apr 22nd 2011, 09:38 AM
emakarov
Quote:

Originally Posted by stripe501
I would like someone to explain how(a^3-b^3)*(c/a-b) evaluates to c*(a^2+ab+b^2)

It does not, but (a^3-b^3)*c/(a-b) does.
• Apr 22nd 2011, 10:11 AM
topsquark
Quote:

Originally Posted by stripe501
I would like someone to explain how(a^3-b^3)*(c/a-b) evaluates to c*(a^2+ab+b^2)

You do it like the rest of us have had to. Multiply out (a - b)*(a^2 + ab + b^2) = a^3 - b^3 and note it for reference the next time you see it.

So you get
http://latex.codecogs.com/png.latex?... b^3)c}{a - b}

http://latex.codecogs.com/png.latex?...2 + ab + b^2)c

-Dan
• Apr 22nd 2011, 10:26 AM
bjhopper
Algebra problem
Hi stripe501,
A fulcrum is a support or wedge about which a lever turns
A frustum is part of a conical or pyramid object formed by cutting off apart of the top parallel to the base.Your equation does not appear to address either one of these shapes

bjh