Final answer:
The factored form of r³ - r² is r²(r - 1), where r² is factored out as the greatest common factor.
Step-by-step explanation:
The factored expression for r³ - r² can be found by factoring out the greatest common factor, which in this case is r². Taking r² out of each term, we are left with:
r²(r - 1)
This expression indicates that we can express the original polynomial as the product of r² and r subtracted by 1. The factoring technique used here is helpful in many mathematical applications, including the study of pipeline flow where expressions like these may represent cross-sectional areas or other related concepts. For instance, the equation Q = A∆r², where Q is the flow rate and A∆r² is the cross-sectional area of the hose, demonstrates the use of r² in practical applications related to fluids.