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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