In the expansion of (2x + 1y)^10, find the coefficient of x^5y^5.
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(10,k)(2x)^(10-k)(y)^k. For k=5, the coefficient is C(10,5)·2^5·1^5=8064. Remember that the numerical coefficient comes from the binomial coefficient and the constants attached to x and y, including any negative sign.
