Question

What is the quotient when r^6−p^6 is divided by the product of r^2+rp+p^2 and r−p?

a. r^3 - p^2
b. r^3 - p^3
c. r^3 + p^2
d. r^3 + p^3

Answer 1

r³ + p³

Explanation:

product of r²+rp+p² & r-p:

(r²+rp+p²)(r-p)

= r³ + r²p + rp² - r²p - rp² - p³

= r³ - p³

r⁶ - p⁶ = (r³)² - (p³)²

= (r³ + p³)(r³ - p³)

quotient:

(r⁶ - p⁶) ÷ (r³ - p³)

= (r³ + p³)(r³ - p³) ÷ (r³ - p³)

= r³ + p³