Question

Упростите выражение 1)
$(x + 2)( {x}^{2} - 2x + 4) - x(x - 3)(x + 3)$
2)
$(a + 1)(a - 1)( {a}^{2} - a + 1)( {a}^{2} + a + 1)( {a}^{6} + 1)( {a}^{12} + 1)( {a}^{24} + 1)$



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Answer 1

$(x+2)(x^2 - 2x + 4) - x(x-3)(x+3) = x^3 + 2^3 - x(x^2 - 3^2) =$

$= x^3 + 8 - x(x^2 - 9) = x^3 + 8 - x^3 + 9x = 8 + 9x$

$(a+1)(a-1)(a^2 - a + 1)(a^2 + a + 1)(a^6 + 1)(a^{12} + 1)(a^{24} + 1) =$

$= (a^3 + 1^3)(a^3 - 1^3)(a^6 + 1)(a^{12}+1)(a^{24} + 1) =$

$= (a^6 - 1)(a^6 + 1)(a^{12} + 1)(a^{24} + 1) = (a^{12} - 1)(a^{12}+1)(a^{24} + 1) =$

$= (a^{24} - 1)(a^{24} + 1) = a^{48} - 1$.