How do you use the Binomial Theorem to expand #(d-5)^6#?

1 Answer
Jul 20, 2017

Answer:

#d^6-30d^5-2500d^3+9375d^2-18750d+15625#

Explanation:

#(d+(-5))^6=((6),(0))d^6(-5)^0+((6),(1))d^5(-5)^1+#

#((6),(2))d^4(-5)^2+((6),(3))d^3(-5)^3+((6),(4))d^2(-5)^4+#

#((6),(5))d^1(-5)^5+((6),(6))d^0(-5)^6=#

#(6!)/(0!(6-0)!)d^6-5(6!)/(1!(6-1)!)d^5+25(6!)/(2!(6-2)!)d^4+#

#-125(6!)/(3!(6-3)!)d^3+625(6!)/(4!(6-4)!)d^2-3125(6!)/(5!(6-5)!)d+#

#15625(6!)/(6!(6-6)!)=#

#d^6-5*6d^5+25*15d^4-125*20d^3+625*15d^2-#

#3125*6d+15625=#

#d^6-30d^5-2500d^3+9375d^2-18750d+15625#