espandere (5(-2n+k)^3)/(8n^3)

Soluzione

espandere

\frac{5 ( - 2 n + k ) ^{3}}{8 n ^{3}}

- 5 + \frac{15 k}{2 n} - \frac{15 k ^{2}}{4 n ^{2}} + \frac{5 k ^{3}}{8 n ^{3}}

Fasi della soluzione

\frac{5 ( - 2 n + k ) ^{3}}{8 n ^{3}}

(- 2 n + k)^{3} = - 8 n^{3} + 12 n^{2} k - 6 n k^{2} + k^{3}

= \frac{5 ( - 8 n ^{3} + 12 n ^{2} k - 6 n k ^{2} + k ^{3} )}{8 n ^{3}}

Espandi

5 (- 8 n^{3} + 12 n^{2} k - 6 n k^{2} + k^{3}) : - 40 n^{3} + 60 n^{2} k - 30 n k^{2} + 5 k^{3}

= \frac{- 40 n ^{3} + 60 n ^{2} k - 30 n k ^{2} + 5 k ^{3}}{8 n ^{3}}

Applica la regola delle frazioni:

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

\frac{- 40 n ^{3} + 60 n ^{2} k - 30 n k ^{2} + 5 k ^{3}}{8 n ^{3}} = - \frac{40 n ^{3}}{8 n ^{3}} + \frac{60 n ^{2} k}{8 n ^{3}} - \frac{30 n k ^{2}}{8 n ^{3}} + \frac{5 k ^{3}}{8 n ^{3}}

= - \frac{40 n ^{3}}{8 n ^{3}} + \frac{60 n ^{2} k}{8 n ^{3}} - \frac{30 n k ^{2}}{8 n ^{3}} + \frac{5 k ^{3}}{8 n ^{3}}

Cancellare

\frac{40 n ^{3}}{8 n ^{3}} : 5

= - 5 + \frac{60 n ^{2} k}{8 n ^{3}} - \frac{30 n k ^{2}}{8 n ^{3}} + \frac{5 k ^{3}}{8 n ^{3}}

Cancellare

\frac{60 n ^{2} k}{8 n ^{3}} : \frac{15 k}{2 n}

= - 5 + \frac{15 k}{2 n} - \frac{30 n k ^{2}}{8 n ^{3}} + \frac{5 k ^{3}}{8 n ^{3}}

Cancellare

\frac{30 n k ^{2}}{8 n ^{3}} : \frac{15 k ^{2}}{4 n ^{2}}

= - 5 + \frac{15 k}{2 n} - \frac{15 k ^{2}}{4 n ^{2}} + \frac{5 k ^{3}}{8 n ^{3}}

e x p an d (x - \frac{π}{4}) sin (2 x)

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