What is the coefficient of: x^7y^12 in (2x+3y)^19
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What is the coefficient of: x^7y^12 in (2x+3y)^19

[From: ] [author: ] [Date: 12-05-13] [Hit: ]
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general term, T(r+1) ( a + b)^n = nCr (a)^(n-r) (b)^r

since we are looking for x^7 and y^12, n - r = 7 and r = 12

13 the term in the expansion of (2x + 3y)^19 will have the coefficient of x^7 y^12

T13 = 19C12 (2x)^7 (3y)^12

= (19*18*17*16*15*14*13 /7*6*5*4*3*2) (2)^ 7 (3)^12 x^7 y^12

= 3427615885824

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Binomial expansion: The term where x^k occurs is (19Ck) (2x)^k (3y)^(19-k).

The term where x^7 occurs is (19C7) * (2x)^7 * (3y)^12.
Combine all the constants together to get your answer.
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