\(\left(2x-1\right)^7-\left(2x-1\right)^5=0\Leftrightarrow\left(2x-1\right)^5\left[\left(2x-1\right)^2-1\right]=0\)
\(\Leftrightarrow\left(2x-1\right)^5\left(2x-1-1\right)\left(2x-1+1\right)=0\)
\(\Leftrightarrow\left(2x-1\right)^5\left(2x-2\right)2x=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(2x-1\right)^5=0\\2x-2=0\\2x=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=1\\x=0\end{matrix}\right.\)
\(\left(2x-1\right)^7-\left(2x-1\right)^5=0\)
\(\Leftrightarrow\left(2x-1\right)^5\left(\left(2x-1\right)^2-1\right)=0\)
\(\Leftrightarrow\left(2x-1\right)^5\left(4x^2-4x+1-1\right)=0\)
\(\Leftrightarrow\left(2x-1\right)^5\left(4x^2-4x\right)=0\)
\(\Leftrightarrow\left(2x-1\right)^54x\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\x-1=0\\x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=1\\x=0\end{matrix}\right.\)
