so that our equation has roots in 1 and -1 we are going to express the polynomial in the factored form
so
[tex]y=a(x-b)(x-c)[/tex]where a is the coefficient, b and c the roots
so replacing
[tex]\begin{gathered} y=2(x-(-1))(x-(1)) \\ \\ y=2(x+1)(x-1) \end{gathered}[/tex]then solve the multiplication
[tex]\begin{gathered} y=2((x\times x)+(x\times-1)+(1\times x)+(1\times-1)) \\ y=2(x^2-x+x-1) \\ y=2x^2-2 \end{gathered}[/tex]