What is (x^2-1/(x^2))(x^2+1/(x^2)) ?

The solution to (x^2-1/(x^2))(x^2+1/(x^2)) is ((x^4-1)(x^4+1))/(x^4)

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simplify (x^2-1/(x^2))(x^2+1/(x^2))

simplify

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

\frac{( x ^{4} - 1 ) ( x ^{4} + 1 )}{x ^{4}}

Solution steps

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

Join

x^{2} - \frac{1}{x ^{2}} : \frac{x ^{4} - 1}{x ^{2}}

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

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Simplify

(x^{4} - 1) (x^{2} + \frac{1}{x ^{2}}) : \frac{( x ^{4} - 1 ) ( x ^{4} + 1 )}{x ^{2}}

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

Apply the fraction rule:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

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

Simplify

x^{2} x^{2} : x^{4}

= \frac{( x ^{4} - 1 ) ( x ^{4} + 1 )}{x ^{4}}

(cos (β) - 1) (sin (β) - 1)

(s + 170) (s^{2} - 2025) (s + 20 π)

(2 + cos (2 θ))^{2}

(3 x + \frac{\frac{5}{6}}{x})^{8}

6 (\frac{x ^{2}}{2} - \frac{x ^{3}}{3})

What is (x^2-1/(x^2))(x^2+1/(x^2)) ?
The solution to (x^2-1/(x^2))(x^2+1/(x^2)) is ((x^4-1)(x^4+1))/(x^4)