What is the coefficient of x^4 in the expansion of (x+3)^7
Start by expanding (a+b)7, using Pascal's Triangle or the binomial coefficient function to work out the coefficients:a7 + 7a6b + 21a5b2 + 35a4b3 + 35a3b4 + 21a2b5 + 7ab6 + b7 , where a=x and b=3As the question wants the coefficient of x3, we need to look for a3 . The expansion gives 35a3b4, so we must substitute values in for a and b. As stated earlier, a=3 and b=3, hence; 35a3b4 = 35 * x3 * 34 = 35 * 81 * x3 = 2835x3Therefore the coefficient of x3 is 2835
