Question

Wyatt is asked to prove the polynomial identity a³ - b³. Which of the following expressions is the equivalent form of this identity?

a. (a + b) (a² - ab + b²)
b. (a - b) (a² + ab + b²)
c. (a - b) (a² - ab + b²)
d. (a - b) (a² - ab - b²)

Answer 1

The correct equivalent expression for proving the polynomial identity a³ - b³ is option b: (a - b)(a² + ab + b²), as it directly matches the factored form of the difference of cubes.

Step-by-step explanation:

To prove the polynomial identity a³ - b³, we need to factor it. We are given four possible equivalent expressions and must determine which is correct. The difference of cubes can be factored as follows:

a³ - b³ = (a - b)(a² + ab + b²)

Now let's match this result to the options provided:

1. (a + b)(a² - ab + b²)
2. (a - b)(a² + ab + b²)
3. (a - b)(a² - ab + b²)
4. (a - b)(a² - ab - b²)

Therefore, the correct equivalent expression for a³ - b³ from the options is option b: (a - b)(a² + ab + b²).