Final answer:
To perform the indicated operation (r s)(r² - rs s²), we need to apply the distributive property of multiplication over addition or subtraction. First, multiply r with r², which gives us r³. Then, multiply r with -rs s², which gives us -r²s³. Next, multiply s with r², which gives us rs². Finally, multiply s with -rs s², which gives us -rs³. Combining these terms, the expression becomes r³ - r²s³ + rs² - rs³.
Step-by-step explanation:
To perform the indicated operation (r s)(r² - rs s²), we need to apply the distributive property of multiplication over addition or subtraction.
First, multiply r with r², which gives us r³. Then, multiply r with -rs s², which gives us -r²s³.
Next, multiply s with r², which gives us rs². Finally, multiply s with -rs s², which gives us -rs³.
Combining these terms, the expression becomes r³ - r²s³ + rs² - rs³.