Question

计算：(x+1)(x方+1)(x四次方+1)（x八次方+1）（x的十六次方+1）（x的三十二次方+1）,用x-1/x-1

Answer 1

(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)

=[(x-1)(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)]/(x-1)

=[(x^2-1))(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)]/(x-1)

=[(x^4-1)(x^4+1)(x^8+1)(x^16+1)(x^32+1)]/(x-1)

=[(x^8-1)(x^8+1)(x^16+1)(x^32+1)]/(x-1)

=[(x^16-1)(x^16+1)(x^32+1)]/(x-1)

=[(x^32-1)(x^32+1)]/(x-1)

=(x^64-1)/(x-1)