The coefficient of x3 in the expansion of 1-3x2-1-2xwill be

= (1 + 3x)^2(1 2x)^ 1 = (1 + 3x)^2(1 + 2x + 1.2/2.1( 2x)^2 + .......) = (1 + 6x + 9x^2)(1 + 2x + 4x^2 + 8x^3 +........) Therefore coefficient of x^3 is (8 ...

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Byju's Answer

Standard XII

Mathematics

Expansions of the Form (1+x)^(-n) and (1-x)^(-n)

The coefficie...

Question

The coefficient of $x^{3}$ in the expansion of $\frac{(1 + 3 x)^{2}}{1 - 2 x}$

will be

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None of these

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Solution

The correct option is C
50

= $(1 + 3 x)^{2}$ ( $1 - 2 x)^{- 1}$

= ( $1 + 3 x)^{2}$ (1 + 2x + $\frac{1.2}{2.1} (- 2 x)^{2} + . . . . . . .$ )

= $(1 + 6 x + 9 x^{2}) (1 + 2 x + 4 x^{2} + 8 x^{3} + . . . . . . . .)$

Therefore coefficient of $x^{3}$ is (8 + 24 + 18) = 50.

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The coefficient of x3 in the expansion of (1+3x)21−2x will be

The correct option is C 50 = (1+3x)2(1−2x)−1 = (1+3x)2(1 + 2x + 1.22.1(−2x)2+.......) = (1+6x+9x2)(1+2x+4x2+8x3+........) Therefore coefficient of x3 is (8 + 24 + 18) = 50.

The coefficient of $x^{3}$ in the expansion of $\frac{(1 + 3 x)^{2}}{1 - 2 x}$

will be

The correct option is C
50

= $(1 + 3 x)^{2}$ ( $1 - 2 x)^{- 1}$

= ( $1 + 3 x)^{2}$ (1 + 2x + $\frac{1.2}{2.1} (- 2 x)^{2} + . . . . . . .$ )

= $(1 + 6 x + 9 x^{2}) (1 + 2 x + 4 x^{2} + 8 x^{3} + . . . . . . . .)$

Therefore coefficient of $x^{3}$ is (8 + 24 + 18) = 50.