Rewrite \({x}^{2}-1\) in the form \({a}^{2}-{b}^{2}\), where \(a=x\) and \(b=1\).
\[({x}^{2}-{1}^{2})({x}^{2}+5x-6)=0\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[(x+1)(x-1)({x}^{2}+5x-6)=0\]
Factor \({x}^{2}+5x-6\).
Ask: Which two numbers add up to \(5\) and multiply to \(-6\)?
Rewrite the expression using the above.
\[(x-1)(x+6)\]
\[(x+1)(x-1)(x-1)(x+6)=0\]
Solve for \(x\).
Ask: When will \((x+1)(x-1)(x-1)(x+6)\) equal zero?
When \(x+1=0\), \(x-1=0\), \(x-1=0\), or \(x+6=0\)
Solve each of the 4 equations above.
\[x=-6,\pm 1\]
\[x=-6,\pm 1\]
x=-1,1,-6
