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Multinomial Expansion

If 1+2x+ 3x...

Question

If ${(1 + 2 x + {3 x}^{2})}^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{20} x^{20}$ then $a_{1}$ equals

A

10

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B

20

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C

210

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D

420

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Solution

The correct option is B $20$
$(1 + 2 x + 3 x^{2})^{10}$
$= 1 +^{10} C_{1} (2 x + 3 x^{2})^{1} +^{10} C_{2} (2 x + 3 x^{2})^{2} . . . +^{10} C_{10} (2 x + 3 x^{2})^{10}$
Here $a_{1}$ is the coefficient of $x$ .
Therefore.
$a_{1} = 2^{10} C_{1}$
$= 2 (10)$
$= 20$

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Similar questions

{(1 + 2 x + 3 x^{2})}^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . . . + a_{20} x^{20}

a_{1}

{(1 + 2 x + 3 x^{2})}^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . . + a_{20} x^{20}

(1 + 2 x + 3 x^{2})^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{20} x^{20}

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(1 + 2 x + 3 x^{2})^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{20} x^{20},

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{(1 + x + 2 x^{2})}^{20} = a_{0} + a_{1} x + a_{2} x^{2} + . . . . + a_{39} x^{39} + a_{40} x^{40}

then find the value of

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