How do you use the binomial series to expand #(1 + 4x)^-3#?

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Answer 1 · 2016-03-01T11:07:55

#(1+4x)^-3=1/(1+4x)^3=1/(1+12x+48x^2+64x^3)#

#(a+b)^3=a^3+3a^2b+3ab^2+b^3#

We let #a=1# and #b=4x#

and

#(1+4x)^3=(1)^3+3(1)^2(4x)+3(1)(4x)^2+(4x)^3#

#(1+4x)^3=1+12x+48x^2+64x^3#

This will be the denominator of #1/(1+4x)^3#

God bless....I hope the explanation is useful.