desarrollar (3(2-z)^5)/(10)

Solución

desarrollar

\frac{3 ( 2 - z ) ^{5}}{10}

- \frac{3 z ^{5}}{10} + 3 z^{4} - 12 z^{3} + 24 z^{2} - 24 z + \frac{48}{5}

Pasos de solución

\frac{3 ( 2 - z ) ^{5}}{10}

(2 - z)^{5} = 32 - 80 z + 80 z^{2} - 40 z^{3} + 10 z^{4} - z^{5}

= \frac{3 ( - z ^{5} + 10 z ^{4} - 40 z ^{3} + 80 z ^{2} - 80 z + 32 )}{10}

Expandir

3 (32 - 80 z + 80 z^{2} - 40 z^{3} + 10 z^{4} - z^{5}) : 96 - 240 z + 240 z^{2} - 120 z^{3} + 30 z^{4} - 3 z^{5}

= \frac{96 - 240 z + 240 z ^{2} - 120 z ^{3} + 30 z ^{4} - 3 z ^{5}}{10}

Aplicar las propiedades de las fracciones:

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

\frac{96 - 240 z + 240 z ^{2} - 120 z ^{3} + 30 z ^{4} - 3 z ^{5}}{10} = \frac{96}{10} - \frac{240 z}{10} + \frac{240 z ^{2}}{10} - \frac{120 z ^{3}}{10} + \frac{30 z ^{4}}{10} - \frac{3 z ^{5}}{10}

= \frac{96}{10} - \frac{240 z}{10} + \frac{240 z ^{2}}{10} - \frac{120 z ^{3}}{10} + \frac{30 z ^{4}}{10} - \frac{3 z ^{5}}{10}

\frac{96}{10} = \frac{48}{5}

\frac{240 z}{10} = 24 z

\frac{240 z ^{2}}{10} = 24 z^{2}

\frac{120 z ^{3}}{10} = 12 z^{3}

\frac{30 z ^{4}}{10} = 3 z^{4}

= \frac{48}{5} - 24 z + 24 z^{2} - 12 z^{3} + 3 z^{4} - \frac{3 z ^{5}}{10}

Reescribir en la forma estándar

= - \frac{3 z ^{5}}{10} + 3 z^{4} - 12 z^{3} + 24 z^{2} - 24 z + \frac{48}{5}

e x p an d \frac{980 π + 114 ( 2 + 3 )}{14 π}

e x p an d (- 2 x + sy (x, s, o) = o) \cdot s

e x p an d \frac{x ^{2}}{( 1 + x ) ( 2 x + 1 )}

e x p an d \frac{s}{( ( x ^{2} + 9 ) \cdot ( x ^{2} + 4 ) )}

e x p an d (1 + 2 x)^{(\frac{1}{2})}