SOLUTION: I have been struggling with this math problem for awhile now and I was wondering if anyone could help me? I would deeply appreciate it!! Please and Thank You!! Power of Monomi

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Question 130956This question is from textbook Algebra Structure and Method
: I have been struggling with this math problem for awhile now and I was wondering if anyone could help me? I would deeply appreciate it!! Please and Thank You!!
Power of Monomials
find and simplify (a) the sum and (b) the product of the given monomials
(2x)^3(xy)^2,(2xy)^2(-x)^3

This question is from textbook Algebra Structure and Method

Found 2 solutions by checkley71, emp233:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
the sum:
(2x)^3(xy)^2=(8x^3)(x^2y^2)=8x^5y^2
(2xy)^2(-x)^3=(4x^2y^2)(-x^3)=-4x^5y^2
8x^5y^2
-4x^5y^2 now add.
----------------
4x^5y^2 answer for the sum.
---------------------------------------------------------------
8x^5y^2
-2x^5y^2 now multiply
---------------------------------
-16x^10y^4 answer for the product.

Answer by emp233(1) About Me  (Show Source):
You can put this solution on YOUR website!
This is the solution of your problem, first of all solve the powers
%282x%29%5E3=8x%5E3
%28xy%29%5E2=x%5E2y%5E2
%282xy%29%5E2=4x%5E2y%5E2
%28-x%29%5E3=-x%5E3
Then to solve the sum you just make 8x%5E3%2A%28x%5E2y%5E2%29+4x%5E2%2A%28-x%5E3%29
=8x%5E5y%5E2-4x%5E5y%5E2=4
And to solve the product you just look at the two resulting monomials
8x%5E5y%5E2 and -4x%5E5y%5E2 and just make the multiplication %288x%5E5y%5E2%29%2A%28-4x%5E5y%5E2%29=32x%5E5y%5E2