If a + b = –1, then evaluate a3 + b3 – 3ab

The given expression a^3 + b^3 - 3ab can be rewritten as (a + b)(a^2 + b^2 - ab) using the formula for the sum of cubes.

Given that a + b = -1, we can substitute this into the expression to get:

(-1)(a^2 + b^2 - ab)

Now, we need to find the value of a^2 + b^2 - ab. We can do this by squaring the given equation a + b = -1 to get:

(a + b)^2 = (-1)^2 a^2 + 2ab + b^2 = 1

Since we want a^2 + b^2 - ab, we can rearrange this equation to solve for that:

a^2 + b^2 - ab = 1 - 3ab

Substitute a + b = -1 into this equation to get:

1 - 3(-1) = 1 + 3 = 4

So, a^3 + b^3 - 3ab = (-1)(4) = -4.