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Find the coefficient of x^5 in the expansion of (1+x^2)^5(1+x)

Question

Find the coefficient of $x^{5}$ in the expansion of $(1 + x^{2})^{5} (1 + x)^{4}$

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Jack Discussed

Find the coefficient of

x^{5}

in the expansion of

(1 + x^{2})^{5} (1 + x)^{4}

5 mins ago

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5 mins ago

Text solutionVerified

(1 + x^{2})^{5} (1 + x)^{4}

\Rightarrow [^{5} C_{0} +^{5} C_{1} x^{2} +^{5} C_{2} x^{4} ....] [^{4} C_{0} +^{4} C_{1} x +^{4} C_{2} x^{2} ....]

\Rightarrow^{5} C_{1}^{4} C_{3} x^{5} +^{5} C_{2}^{4} C_{1} x^{5}

\Rightarrow [5 \times 4 + 10 \times 4] x^{5}

\Rightarrow [20 + 40] x^{5}

\Rightarrow 60 x^{5}

Hence, the answer is

60 x^{5} .

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Question Text	Find the coefficient of $x^{5}$ in the expansion of $(1 + x^{2})^{5} (1 + x)^{4}$
Answer Type	Text solution:1
Upvotes	150