Given f(x)=(x^3-7)*(x+4)^5, find the term x^3 of f(x).

Before starting to solve this problem, student should acknowledge that there are more than a variable, which satisfies the condition x^3. There are two ways to obtain this answer: (1) x^3 in the first multiple is multiplied by the constant in the second multiple; (2) -7 multiplied by the term x^3 with some coefficient, which should be obtained after expanding and simplifying the binomial theorem. The correct answer would be (1)+(2). 

Bearing this in mind, the first step should be using binomial theorem to expand and simplify the equation.Since we are looking for the constant (x^0) and x^3 terms, even without simplifying the whole expression, the correct answer can be found. The constant is the last term in the expression with x^0, nCr(5,0)=1, hence 41=4; and the term with x^3 is the 3rd term, nCr(5,3)=10, 10x^34^2=160x^3

(1) => 4x^3 and (2) => -7160x^3=-112x^3 

Hence, the correct answer is (4-112)x^3= -108x^3.