What is factor 4x^{2n}-1/5 ?

The solution to factor 4x^{2n}-1/5 is (2x^n+sqrt(1/5))(2x^n-sqrt(1/5))

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factor 4x^{2n}-1/5

factor

4 x^{2 n} - \frac{1}{5}

(2 x^{n} + \frac{1}{5}) (2 x^{n} - \frac{1}{5})

Solution steps

4 x^{2 n} - \frac{1}{5}

Rewrite

4 x^{2 n}

(2 x^{1 n})^{2}

= (2 x^{1 \cdot n})^{2} - \frac{1}{5}

Apply radical rule:

a = (a)^{2}

\frac{1}{5} = (\frac{1}{5})^{2}

= (2 x^{1 n})^{2} - (\frac{1}{5})^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(2 x^{1 n})^{2} - (\frac{1}{5})^{2} = (2 x^{1 n} + \frac{1}{5}) (2 x^{1 n} - \frac{1}{5})

= (2 x^{1 n} + \frac{1}{5}) (2 x^{1 n} - \frac{1}{5})

Refine

= (2 x^{n} + \frac{1}{5}) (2 x^{n} - \frac{1}{5})

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What is factor 4x^{2n}-1/5 ?
The solution to factor 4x^{2n}-1/5 is (2x^n+sqrt(1/5))(2x^n-sqrt(1/5))