The coefficient of x4
in the expansion of
(1 + x + x2
+ x3)6
in powers of x, is ______.
Answer (integer)
120
Solution
(1 + x + x<sup>2</sup>
+ x<sup>3</sup>)<sup>6</sup>
<br><br>= ((1 + x) (1 + x<sup>2</sup>))<sup>6</sup>
<br><br>= (1 + x)<sup>6</sup>(1 + x<sup>2</sup>)<sup>6</sup>
<br><br>= $\sum\limits_{r = 0}^6 {{}^6{C_r}.{x^r}}$ $\sum\limits_{r = 0}^6 {{}^6{C_r}.{x^{2r}}}$
<br><br>Coefficient of x<sup>4</sup> = <sup>6</sup>C<sub>0</sub>
<sup>6</sup>C<sub>2</sub> + <sup>6</sup>C<sub>2</sub>
<sup>6</sup>C<sub>1</sub> + <sup>6</sup>C<sub>4</sub>
<sup>6</sup>C<sub>0</sub> = 120
About this question
Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion
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