What is expand (z-1/z)^4 ?

The solution to expand (z-1/z)^4 is z^4-4z^2+6-4/(z^2)+1/(z^4)

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expand (z-1/z)^4

expand

(z - \frac{1}{z})^{4}

z^{4} - 4 z^{2} + 6 - \frac{4}{z ^{2}} + \frac{1}{z ^{4}}

Solution steps

(z - \frac{1}{z})^{4}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = z, b = - \frac{1}{z}

= i = 0 \sum 4 (i 4) z^{(4 - i)} (- \frac{1}{z})^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} z^{4} (- \frac{1}{z})^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} z^{3} (- \frac{1}{z})^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} z^{2} (- \frac{1}{z})^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} z^{1} (- \frac{1}{z})^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} z^{0} (- \frac{1}{z})^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} z^{4} (- \frac{1}{z})^{0} : z^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} z^{3} (- \frac{1}{z})^{1} : - 4 z^{2}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} z^{2} (- \frac{1}{z})^{2} : 6

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} z^{1} (- \frac{1}{z})^{3} : - \frac{4}{z ^{2}}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} z^{0} (- \frac{1}{z})^{4} : \frac{1}{z ^{4}}

= z^{4} - 4 z^{2} + 6 - \frac{4}{z ^{2}} + \frac{1}{z ^{4}}

\frac{80}{0.07} (1 - \frac{1}{( 1.035 ) ^{10}}) + \frac{1000}{1.03 5 ^{10}}

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3 (sin^{6} (θ) + cos^{6} (θ)) + 9 sin^{2} (θ) cos^{2} (θ)

x^{\frac{1}{3}} (x^{2} - 70)

sin (t) u (t - 2 π)

What is expand (z-1/z)^4 ?
The solution to expand (z-1/z)^4 is z^4-4z^2+6-4/(z^2)+1/(z^4)