Find the product. (r + s)2 r² + 2rs + s r² + 2rs + s² r² + 2rs + 2s²

Hey there!

For this problem, all you need to remember is the fact that as long as two terms with the same variable(s) (for example, x or y in the place of a number in a term or equation) that you can combine the two by adding/subtracting the coefficients (for example, 3 in the term 3x). Feel free to arrange the terms so that the matching ones are next to each other, since it doesn't matter what order the terms are in for addition. 

The other thing to remember is the distributive property, which applies to the first set of terms, (r+s)2r². You can put the 2r² in front of the (r+s) to make it a little easier to see and distribute, then you multiply the 2r² by r and s to combine these terms. For reference/example, s*s equals s². 

Using that information, you can combine like terms:

2r²(r + s) + 2rs + sr² + 2rs + s²r² + 2rs + 2s²
(2r³ + 2r²s) + 2rs + 2rs + 2rs + s²r² + sr² + 2s²
2r³ + 2r²s + 6rs + s²r² + sr² + 2s²

I forget the rules for what order the terms should be in, so see if there's any information from your lesson material that says this information. This is just a rough guess on how the final equation should look:

2r³ + s²r² + 2r²s + sr² + 2s² + 6rs

Hope this helped you out! :-)