Question

Find continued product of $(x-\frac{1}{x})(x+\frac{1}{x})(x^2-\frac{1}{x^2})$.

Answer 1

$(x-\frac{1}{x})(x+\frac{1}{x})(x^2-\frac{1}{x^2})$

$=\left[\right(x{)}^2-\left(\frac{1}{x^2}{)}^2\right](x^2-\frac{1}{x^2})$

$=(x^2-\frac{1}{x^2})(x^2-\frac{1}{x^2})$

$=(x^2-\frac{1}{x^2}{)}^2$

$(a-b{)}^2=a^2+b^2-2ab$

$=(x^2{)}^2+(\frac{1}{x^2}{)}^2-2.x^2.\frac{1}{x^2}$

$=x^4+\frac{1}{x^4}-2$