The first known statement of this lemma in the modern form is attributed to Pascal, who is also the namesake of a certain device to express its coefficients for positive integer powers.
The Leibnitz identity allows generalization of the product rule in terms of this principle. The q-analog of this law has Gaussian polynomials as its coefficients, and the normal coefficients of this are often stated in a notation resembling a two-vector and can be extended to non-integer powers by using the gamma function instead of the factorial. The first known statement of this lemma in the modern form is attributed to Pascal, who is also the namesake of a certain device to express its coefficients for positive integer powers. For 10 points, identify the theorem that allows the expression of the nth [ennth] power of the sum of two numbers, x and y, as  [the sum from kay equals zero to enn of enn choose kay times ecks to the kay times why to the enn minus kay], which is often used to find coefficients for the expansions of two-variable polynomials.
The Leibnitz identity allows generalization of the product rule in terms of this principle.
{binomial} theorem