What is the coefficient of #x^3# in #(x-1)^3(3x-2)#?

2 Answers
Shwetank Mauria
Mar 13, 2018

The coefficient of #x^3# is #-11#.

Explanation:

The term containing #x^3# in #(x-1)^3(3x-2)# can come in two ways.

One, when we multiply #-2# with the term containing #x^3# in the expansion of #(x-1)^3#. As its expansion is #x^3-3x^2+3x-1#, in the expansion term containing #x^3# is #x^3#. Multipying it with #-2# leads to #-2x^3#.

Two, when we multiply #3x# with the term containing #x^2# in the expansion of #(x-1)^3#, which is #-3x^2#. Multipying it with #3x# leads to #-9x^3#.

As they add up to #-11x^3#, the coefficient of #x^3# is #-11#.

Areej J.
Mar 13, 2018

#x^3=-11#

Explanation:

#=(x-1)^3(3x-2)#
#=(x^3-1-3x(x-1))(3x-2)# (By Applying Formula)
#=(x^3-1-3x^2+3x)(3x-2)#
#=(3x^4-3x-9x^3+9x^2-2x^3+2+6x^2-6x)#
#=3x^4color(red)(-11^3)-9x+15x^2+2#
#=color(red)(-11x^3)#(Coeffficient of #x^3#)

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