The expression $(a - b)^3$ can be expanded using the binomial theorem or by multiplying it step by step. Here's the expansion:

$(a - b)^3 = (a - b)(a - b)(a - b)$

Now, applying the distributive property (or FOIL method for the first two terms) step by step:

1. First, expand $(a - b)(a - b)$:

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

2. Then, multiply the result by $(a - b)$:

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

Now, distribute each term in $(a^2 - 2ab + b^2)$ by $(a - b)$:

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

Expanding each term:

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

Combining like terms:

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

Therefore, the expanded form of $(a - b)^3$ is:

$(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$

Would you like to go over the steps in more detail or have any questions? Here are some related questions:

1. What is the expanded form of $(a + b)^3$?
2. How can we expand $(a - b)^4$?
3. How does the binomial theorem apply to higher powers of binomials?
4. What are the coefficients in the expansion of $(a - b)^n$ for various $n$?
5. How can we factor the expression $a^3 - 3a^2b + 3ab^2 - b^3$?

Tip: When expanding binomials, remember the pattern of coefficients follows Pascal's Triangle, which can help simplify calculations for higher powers!