Question

Which of the following is a factor in the general formula for factoring the difference of cubes?

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

Answer 1

The correct factor in the general formula for factoring the difference of cubes is option 1: (a^2 + ab + b^2), which forms part of the expanded formula (a - b)(a^2 + ab + b^2).

Step-by-step explanation:

The formula for factoring the difference of cubes is a3 - b3 = (a - b)(a2 + ab + b2). So, when looking for the correct factor that accompanies (a - b) in this formula, the correct choice is option 1: (a2 + ab + b2). Let's verify this with an example:

Suppose we have x3 - 8. This is a difference of cubes since 8 is 23. Using the formula, we can factor it as:

(x - 2)(x2 + 2x + 4)

Here, you can see that the trinomial component is indeed of the form a2 + ab + b2.