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Find the coefficient of {x}^{{6}}{y}^{{3}}in the expansion of

Question

Find the coefficient of $x^{6} y^{3}$ in the expansion of $(x + 2 y)^{9}$ .

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Noah Discussed

Find the coefficient of

x^{6} y^{3}

in the expansion of

(x + 2 y)^{9}

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Solution:

(r + 1)^{t h}

term in

(x + 2 y)^{9} = C (9, r) x^{n - r} (2 y)^{r} = C (9, r) 2^{r} (x^{9 - r} y^{r})

If we put,

r = 3

Then,

4^{t h}

term ,

T_{4} = C (9, 3) \cdot 2^{3} (x^{6} y^{3})

∴

Coefficient of

(x^{6} y^{3}) = C (9, 3) \cdot 2^{3}

= 8 * \frac{9 * 8 * 7}{3 * 2 * 1} = 672

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Question Text	Find the coefficient of $x^{6} y^{3}$ in the expansion of $(x + 2 y)^{9}$ .
Answer Type	Text solution:1
Upvotes	150