Answer :
Final answer:
To expand the binomial (x - 5y)⁵ using Pascal's triangle, we can use the binomial theorem. The correct expansion is option a. y⁵ - 5y⁴x + 25y³x² - 125y²x³ + 625yx⁴ - 3125x⁵.
Explanation:
To expand the binomial (x - 5y)⁵ using Pascal's triangle, we will use the binomial theorem. The binomial theorem states that (a + b)ⁿ can be expanded as aⁿ + (nC1) * aⁿ⁻¹ * b + (nC2) * aⁿ⁻² * b² + ... + bⁿ, where n is the exponent and nCk represents the binomial coefficient.
In this case, we have (x - 5y)⁵. To expand it, we will substitute x and y into the formula, using the binomial coefficient for each term.
The correct expansion is option a. y⁵ - 5y⁴x + 25y³x² - 125y²x³ + 625yx⁴ - 3125x⁵.