Final answer:
(a - b)(a² + ab²) is equivalent to a³+ b³, so the correct answer is 3) (a - b)(a² + ab²).
Step-by-step explanation:
This formula is known as the difference of cubes formula. It states that the difference of two cubes can be factored as the product of the difference of the two numbers and the sum of their squares.
In this case, a³ and b³ are the two cubes. Their difference is a³ - b³. The difference of a and b is a - b. The sum of their squares is a² + b².
Therefore, we can write:
a³ - b³ = (a - b)(a² + b²)
The other three expressions are not equivalent to a³ b³.
Expression 1 is a³ + a²b + ab² - a²b - ab² - b³. This expression simplifies to a³ - b³, but it is not factored as the product of two terms.
Expression 2 is (ab)(a² - ab²). This expression simplifies to a³ - b³, but it is not factored as the product of the difference of two terms.
Expression 4 is (ab)(a³ + b³). This expression simplifies to a⁴b + b⁴, which is not equivalent to a³ b³.
So the correct answer is 3) (a - b)(a² + ab²).
Correct question is:
Which of the following expressions is equivalent to a³ b³?
1) a³ + a²b + ab² - a²b - ab² - b³
2) (ab)(a² - ab²)
3) (a - b)(a² + ab²)
4) (ab)(a³ + b³)