Which polynomial identity will prove that 35 = 27 + 8?
Difference of Squares
Difference of Cubes
Sum of Cubes
Square of a Binomial

Solution:

Given, 35 = 27 + 8

⇒ 35 = 3³ + 2³ , which is sum of cubes

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).

Which polynomial identity will prove that 35 = 27 + 8?

Summary:

The polynomial identity which will prove that 35 = 27 + 8 is, sum of cubes.