Question

What is the form of the Sum of Cubes identity?

A. a³ + b³ = (a−b) (a² - ab + b²)
B. a³b³ = (a + b) (a² + ab + b²)
O c. a³ + b³ = (a−b) (a² + ab + b²)
OD. a³ b³ = (a - b) (a² + ab + b²)

Answer 1

a³ + b³ = (a+b) (a² - ab + b²)

Explanation:

(a+b) (a² - ab + b²) =

(a+b)*a² - (a+b)*ab + (a+b)*b² =

(a³+ba²) - (a²b+ab²) + (ab²+b³) =

a³ + ba² - a²b - ab² + ab² + b³ =

a³ + ba² - a²b - ab² + ab² + b³ =

a³ + 0 - 0 + b³ = a³ + b³