Use pascal's triangle to expand the binomial. (d-5)^6 show it step by step with explanations.

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

Step-by-step explanation:

Suppose you have (x + y)^6, the numbers  in the 6th row of Pascal's triangle are the coefficients of the terms in a sixth order polynomial.

In the figure attached, Pascal's triangle is shown.

The coefficients are 1, 6, 15, 20, 15, 6,1. Then:

(x + y)^6 =  x^6 + 6*x^5*y + 15*x^4*y^2 + 20*x^3*y^3 + 15*x^2*y^4 + 6*x*y^5+ y^6

Replacing x = d and y = -5:

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