(3^2017+3^-2017)²-(3^2017-3^-2017)²

[tex]( {3}^{2017} + {3}^{ - 2017} ) - ( {3}^{2017} - {3}^{ 2017} ) \\ \ = ( {3}^{2017} + {3}^{ - 2017} + {3}^{2017} - {3}^{ - 2017} )( {3}^{2017} + {3}^{ - 2017} - {3}^{2017} + {3}^{ - 2017} ) \\ =( 2 \times {3}^{2017} )(2 \times {3}^{ - 2017} ) \\ = 4 \times {3}^{0} \\ = 4[/tex]
note
a²-b² = (a+b)(a-b)