Question

Use the Binomial Theorem to find the binomial expansion of the expression.

(d_5)6

Answer 1

By the binomial theorem, the successive binomial coefficients for a 6th power
are:
1, 6, 15, 20, 15, 6, 1

So,
(d-5)^6 = d^6 + 6*d^5*(-5) + 15*d^4*(-5)^2 + 20*d^3*(-5)^3 + 15*d^2*(-5)^4 + 6*d*(-5)^5 + (-5)^6
= d^6 - 30d^5 + 375d^4 - 2500d^3 + 9375d^2 - 18750d + 15625