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

Solution:

Given, 19 = 27 - 8

⇒19 = 3³ - 2³,

Hence the difference of cubes is used.

Therefore option (i) is the answer.

Note:

→ A polynomial in the form a³ - b³ is called a difference of cubes.

The difference of the cubes a³ - b³ = (a - b)(a² + ab + b²).

→ A polynomial in the form a² - b² is called a difference of squares.

The difference of the squares, a² - b² = (a - b)(a + b).

→ A polynomial in the form a³ + b³ is called a sum of cubes.

The sum of the cubes a³ + b³ = (a + b)(a² - ab + b²).

What polynomial identity should be used to prove that 19 = 27 - 8?

Summary:

Polynomial identity which used to prove that 19 = 27 - 8 is the difference of cubes.