Final answer:
To expand the expression (2x-3y)³ using Pascal's triangle, we need to use the binomial theorem. The expanded expression is 8x³ - 36x²y + 54xy² - 27y³.
Step-by-step explanation:
To expand the expression (2x-3y)³ using Pascal's triangle, we need to use the binomial theorem. The binomial theorem states that (a + b)ⁿ = nC₀aⁿb⁰ + nC₁aⁿ⁻¹b¹ + nC₂aⁿ⁻²b² + ... + nCₙa⁰bⁿ, where nCₖ represents the binomial coefficient. In this case, n = 3, a = 2x, and b = -3y.
Using Pascal's triangle, the binomial coefficients for the expansion are 1, 3, 3, and 1. So, the expanded expression is 1(2x)³(-3y)⁰ + 3(2x)²(-3y)¹ + 3(2x)¹(-3y)² + 1(2x)⁰(-3y)³.
Simplifying the terms, we get 8x³ + 12x²(-3y) + 6x(-3y)² + (-3y)³, which can be further simplified to 8x³ - 36x²y + 54xy² - 27y³.