How do you use the Binomial Theorem to expand #(d-3b)^3#?

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Answer 1 · 2017-09-04T06:11:22

The answer is #=d^3-9d^2b+27db^2-27d^3#

#(x+y)^n=((n),(0))x^n+((n),(1))x^(n-1)y+((n),(2))x^(n-2)y^2+........+((n),(n))y^n#

#AA n in NN# and #x,y in RR#

When #n=3#

#(x+y)^3=x^3+3x^2y+3xy^2+y^3#

Therefore,

#(d-3b)^3=d^3+3d^2*(-3b)+3d*(-3d)^2+(-3d)^3#

#=d^3-9d^2b+27db^2-27d^3#