What is expand (t-2/(t^2))^3 ?

The solution to expand (t-2/(t^2))^3 is (t^9-6t^6+12t^3-8)/(t^6)

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expand (t-2/(t^2))^3

expand

(t - \frac{2}{t ^{2}})^{3}

\frac{t ^{9} - 6 t ^{6} + 12 t ^{3} - 8}{t ^{6}}

Solution steps

(t - \frac{2}{t ^{2}})^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(t - \frac{2}{t ^{2}})^{3} = t^{3} - 3 t^{2} \frac{2}{t ^{2}} + 3 t (\frac{2}{t ^{2}})^{2} - (\frac{2}{t ^{2}})^{3}

= t^{3} - 3 t^{2} \frac{2}{t ^{2}} + 3 t (\frac{2}{t ^{2}})^{2} - (\frac{2}{t ^{2}})^{3}

Simplify

t^{3} - 3 t^{2} \frac{2}{t ^{2}} + 3 t (\frac{2}{t ^{2}})^{2} - (\frac{2}{t ^{2}})^{3} : \frac{t ^{9} - 6 t ^{6} + 12 t ^{3} - 8}{t ^{6}}

= \frac{t ^{9} - 6 t ^{6} + 12 t ^{3} - 8}{t ^{6}}

\frac{1}{( s + 1 ) ( s + 3 )}

\frac{( x - 3 ) ^{2} ( 2 x - 3 )}{( x - 4 ) ( x + 2 )}

t^{\frac{5}{2}} (t^{2} - 10 t + 16)

\frac{s + 4}{s ( s + 0.5 ) ( s + 1 ) ( s ^{2} + 0.4 s + 4 )}

(4 + 4 cos (θ))^{2}

What is expand (t-2/(t^2))^3 ?
The solution to expand (t-2/(t^2))^3 is (t^9-6t^6+12t^3-8)/(t^6)