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

(d_5) 6

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