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