Question

4x²-8x+4=2(1-x)(1+x)

Answer 1

\(4x^2-8x+4=2\left(1-x\right)\left(1+x\right)\)

\(\Leftrightarrow4x^2-8x+4=2-2x^2\)

\(\Leftrightarrow6x^2-8x+2=0\)

\(\Leftrightarrow3x^2-4x+1=0\)

\(\Leftrightarrow3x^2-3x-x+1=0\)

\(\Leftrightarrow3x\left(x-1\right)-\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(3x-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-1=0\\3x-1=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{1}{3}\end{matrix}\right.\)