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Popular >

expand (z-1/z)^2

Solution

expand

(z - \frac{1}{z})^{2}

Solution

\frac{z ^{4} - 2 z ^{2} + 1}{z ^{2}}

Solution steps

(z - \frac{1}{z})^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= \frac{z ^{4} - 2 z ^{2} + 1}{z ^{2}}

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Frequently Asked Questions (FAQ)

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