Find the coefficient a of the term in the expansion of the binomial.

Question

Find the coefficient a of the term in the expansion of the binomial

Binomial (z^4-t)¹¹ Term az¹⁶ t⁷

Answer 1

(z⁴ - t)¹¹ = (11_c0)(z⁴)¹¹(-t)⁰ + (11_c1)(z⁴)¹⁰(-t)¹ + (11_c2)(z⁴)⁹(-t)² + .. + (11_c7)(z⁴)⁴(-t)⁷ + ... (11_c11)(z⁴)⁰(-t)¹¹

(11_c7)(z¹⁶)(-t)⁷ = [11! / ((7!)((11-7)!)](z¹⁶)(-t⁷) = -330z¹⁶t⁷