What is the coefficient of $x^4$ in the expansion of $(2x−1)^7$

Question

What is the coefficient of $x^4$ in the expansion of $(2x−1)^7$?

I believe that I am to expand to the power of 7 and then chose the value for which x is to the power of 4.

so:

$7C3(2x^4)(-1)^3$

Which ends up to be:

$-70x^4$

But that answer is incorrect. Where did I go wrong?

Answer 1

Use the binomial theorem and you will find: $-560x^{4}$.
The binomial theorem is: $$\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i$$

Answer 2

An alternative proof is by using Taylor polynomial expansion.

Let $$f(x) = (2x-1)^7$$

The coefficient of $x^4$ is $$\frac {f^{(4)}(0)}{4!} = -560 $$