Final answer:
The expansion of (x - 4y)^3 using the Binomial Theorem involves applying the formula for binomial expansion and utilizing binomial coefficients from Pascal's triangle.
Step-by-step explanation:
To expand (x - 4y)³ using the Binomial Theorem, we need to apply the formula for binomial expansion: (a + b)ⁿ = ∑ₙ=0ⁿ C(n, k)aⁿⁿ¹⁻ₕbₕ. Here, a is x and b is -4y. We will need the binomial coefficients which are the numbers in Pascal's triangle or can be calculated using the combination formula C(n, k). The third row of Pascal's triangle is 1, 3, 3, 1, since we are raising the binomial to the third power (n=3).