In the expansion of (3x + -1y)^8, find the coefficient of x^5y^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(8,k)(3x)^(8-k)(-y)^k. For k=3, the coefficient is C(8,3)·3^5·-1^3=-13608. Remember that the numerical coefficient comes from the binomial coefficient and the constants attached to x and y, including any negative sign.
