What polynomial identity should be used to prove that 19 = 27 - 8? Difference of Cubes. a. Difference of Squares. b. Square of Binomial. c. Sum of Cubes

The answer is Difference of Cubes.

Difference of cubes is a³ - b³.

27 can be written as 3 ³ ( = 3 * 3 * 3 = 27). So, a = 3.

8 can be written as 2³ ( = 2 * 2 * 2 = 8). So, b = 2.

Difference of cubes can be expressed as:

a³ - b³ = (a - b) (a² + ab + b²)

⇒ 3³ - 2³ = (3 - 2) (3² + 3*2 + 2²) = 1 * (9 + 6 + 4) = 1 * 19 = 19

⇒ 27 - 8 = 19