Explanation:
[tex] { {(x}^{2} - 1)}^{3} \\ from \: difference \: of \: squares \\ ( {a}^{2} - {b}^{2} ) = (a - b)(a + b) \\ hence \: { {(x}^{2} - 1)}^{3} = { {(x}^{2} - {1}^{2}) }^{3} \\ = ( {x - 1)}^{3} {(x + 1)}^{3} \\ since \: {(a - b)}^{3} = ( {a}^{3} - {b}^{3} + ab(a - b)) \\ {(a + b)}^{3} = ( {a}^{3} + {b}^{3} + 3ab(a + b)) \\ hence \: \: a = x \\ \: \: \: \: b = 1 \\ substitute \: in \: the \: identities[/tex]
