In the expansion of (3x + 1y)^11, find the coefficient of x^8y^3.
Note
Use the binomial theorem and match the power of y to decide the value of k. Once k is known, the power of x is automatically n-k. The general term is C(11,k)(3x)^(11-k)(y)^k. For k=3, the coefficient is C(11,3)·3^8·1^3=1082565. Remember that the numerical coefficient comes from the binomial coefficient and the constants attached to x and y, including any negative sign.
