Question

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

Answer 1

The answer is Difference of Cubes.

Difference of cubes is a³ - b³.
27 can be written as 3³ (= 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

Answer 2

Answer:

Difference of Cubes

Step-by-step explanation: