Utilizar el teorema del binomio para hallar el coeficiente del término $q^{4} x^{7}$ en la expansión de $(2 q-x)^{11}$

Step 1 ：We are given the expression \((2 q-x)^{11}\) and we need to find the coefficient of the term \(q^{4} x^{7}\) in its expansion.

Step 2 ：We can use the binomial theorem to solve this problem. The binomial theorem states that \((a+b)^n = \sum_{k=0}^{n} {n \choose k} a^{n-k} b^{k}\).

Step 3 ：In this case, \(a=2q\), \(b=-x\), and \(n=11\).

Step 4 ：We want to find the coefficient of the term \(q^{4} x^{7}\), which means \(k=7\) because \(x\) is raised to the power of \(k\). Therefore, we need to find the coefficient of the term where \(a\) is raised to the power of \(n-k=11-7=4\).

Step 5 ：The coefficient will be \({11 \choose 7} (2q)^4 (-x)^7\).

Step 6 ：Calculating this gives us a binomial coefficient of 330 and a coefficient of -5280.

Step 7 ：Final Answer: The coefficient of the term \(q^{4} x^{7}\) in the expansion of \((2 q-x)^{11}\) is \(\boxed{-5280}\).