Question

Упростите выражение (1-х)(1+х)(1+х)(1+х)(1+х)(1+х) - х. Дерзайте!)​

Answer 1

$(1 - x)(1 + x)(1 +x )(1 + x)(1 + x)(1 + x) - x = \\ =( 1 {}^{2} - x {}^{2} )(1 + x) {}^{2} (1 + x) {}^{2} - x = \\ = (1 - x {}^{2} )(1 + x) {}^{4} - x = \\ = (1 - x {}^{2} )(x {}^{4} + 4x {}^{3} + 6x {}^{2} + 4x + 1) - x = \\ = x {}^{4} + 4x {}^{3} + 6x {}^{2} + 4x + 1 - x {}^{6} - 4x {}^{5} - 6x {}^{4} - 4x {}^{3} - x {}^{2} - x = \\ = - 5x {}^{4} + 5x {}^{2} + 3x + 1 - x {}^{6} - 4x {}^{5} = \\ = - x {}^{6} - 4x {}^{5} - 5x {}^{4} + 5x {}^{2} + 3x + 1$