Final answer:
The coefficient of xᵓyⁿ−ᵓ in the expansion of (x+y)ⁿ is indeed equal to ( ᵓₙ), which is a binomial coefficient calculated using the formula n!/(k!(n-k)!). This statement is true.
Step-by-step explanation:
The statement that the coefficient of xᵓyⁿ−ᵓ in the expansion of (x+y)ⁿ equals ( ᵓₙ) is True. In the binomial expansion of (x+y)ⁿ, each term is given by the binomial theorem as ⁿCᵓxⁿ−ᵓyᵓ, where ⁿCᵓ, also denoted as ( ᵓₙ), is the binomial coefficient. It represents the number of ways to choose ᵓ elements from a set of n, and it is calculated using the formula ⁿCᵓ = n!/(k!(n-k)!), where '!' denotes factorial. Thus, for the term xᵓyⁿ−ᵓ, the coefficient is indeed given by ( ᵓₙ).