Answer:
x^3 - 6x^2y + 12xy^2 - 8y^3
Explanation:
We can expand the cube of the binomial (x - 2y) using the binomial theorem, which states that:
(x + y)^n = Σ(n choose k) * x^(n-k) * y^k
where Σ is the summation sign, (n choose k) is the binomial coefficient, and k ranges from 0 to n.
In this case, we have (x - 2y)^3, so we can use n = 3 and substitute x = x and y = -2y to get:
(x - 2y)^3 = Σ(3 choose k) * x^(3-k) * (-2y)^k
Expanding the terms, we get:
(x - 2y)^3 = (3 choose 0) * x^3 * (-2y)^0 + (3 choose 1) * x^2 * (-2y)^1 + (3 choose 2) * x^1 * (-2y)^2 + (3 choose 3) * x^0 * (-2y)^3
Simplifying each term and combining like terms, we get:
(x - 2y)^3 = x^3 - 6x^2y + 12xy^2 - 8y^3
Therefore, the product of (x - 2y)^3 is x^3 - 6x^2y + 12xy^2 - 8y^3.