In the expansion of (2x + -1y)^11, find the coefficient of x^7y^4.
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)(2x)^(11-k)(-y)^k. For k=4, the coefficient is C(11,4)·2^7·-1^4=42240. Remember that the numerical coefficient comes from the binomial coefficient and the constants attached to x and y, including any negative sign.
