The coefficient of x 3 in the expansion of ( 1 + 3 x ) 2 1 − 2 x will be Options: A . &nbsp8 B . &nbsp32 C . &nbsp50 D . &nbspNone of these

Answer: Option C : C = ( 1 + 3 x ) 2 ( 1 − 2 x ) − 1 = ( 1 + 3 x ) 2 (1 + 2x + 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.

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

Question

The coefficient of

x^{3}

in the expansion of

\frac{(1 + 3 x)^{2}}{1 - 2 x}

will be

Options:

A . 8

B . 32

C . 50

D . None of these

Answer: Option C
:
C
=

(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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