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Aratati ca: (x-3)(x+3)( x^{2} +9)( x^{4} +81)( x^{8} + 3^{8} )= x^{16} - 3^{16}

Răspuns :

Alesyo
[tex](x-3)(x+3)( x^{2}+9)( x^{4} +81)( x^{8}+3^{8})= x^{16}-3^{16} (x-3)(x+3)= x^{2}+3x-3x-9= x^{2}-9 (x^{2}-9)( x^{2}+9)= x^{4}+9 x^{2}- 9x^{2}-81= x^{4} -81 (x^{4}-81)( x^{4}+81)= x^{8}+81 x^{4}-81 x^{4}-6561= x^{8}-6561 (x^{8}-6561)( x^{8}+6561)= x^{16}+6561 x^{8}-6561 x^{8}- 3^{16} = x^{16}- 3^{16} REZULTAT x^{16}- 3^{16} = x^{16}- 3^{16} (ADEV)[/tex]

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