Multiplyng Polynomials?

Question

How would you answer this?
(2r-s)(s^2+4r^2-4rs)

Answer 1

multiply each of the 2 terms in 2r - s by each of the 3 terms in s² + 4r² - 4rs, getting 6 terms:

2rs² + 8r³ - 8r²s - s³ - 4r²s + 4rs²

then combine like terms:

8r³ - 12r²s + 6rs² - s³

and the appropriate order is descending powers of r, ascending powers of s.

Answer 2

Treat (s^2 + 4r^2 - 4rs) as a single term, and use the distributive rule twice.

(2r - s)(s^2 + 4r^2 - 4rs) =
2r(s^2 + 4r^2 - 4rs) - s(s^2 + 4r^2 - 4rs) =
(2rs^2 + 8r^3 - 8r^2 s) - (s^3 + 4r^2 s - 4rs^2) =
simplify it from here

Somebody called this the associative rule. It's not. That's something completely different.

Answer 3

multiply each variable..
= 2rs^2-s^3+8r^3-4r^2s-8r^2s
-4rs^2
= 8r^3-2rs^2-12r^2s-s^3

Answer 4

Use the associative law. That says that
a(b+c) = ab+ac

By extension:
(a+b)(c+d) = ac+ad+bc+bd

In words, each term in each bracket needs to be multiplied by each term in the other bracket, then added up (although some of the terms will be negative).