Find the first four terms of the expansion of (1-2x)⁴.

9. The sum of the first four terms in the expansion of $(1-2x)^4$ is equal to the sum of the first three terms in the expansion of $(1-x)^8$. Show that this is true only if $x=0$ or $x=-\frac{1}{4}$.

Step 1: Find the first four terms of the expansion of $(1-2x)^4$.
Using the binomial theorem $(a+b)^n = \binom{n}{0}a^n + \binom{n}{1}a^{n-1}b + \binom{n}{2}a^{n-2}b^2 + \binom{n}{3}a^{n-3}b^3 + \dots$