In the expansion of (1x + -1y)^10, find the coefficient of x^3y^7.
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)(x)^(10-k)(-y)^k. For k=7, the coefficient is C(10,7)·1^3·-1^7=-120. Remember that the numerical coefficient comes from the binomial coefficient and the constants attached to x and y, including any negative sign.
