expandir (((x-2)^5))/5

Solução

expandir

\frac{( ( x - 2 ) ^{5} )}{5}

\frac{x ^{5}}{5} - 2 x^{4} + 8 x^{3} - 16 x^{2} + 16 x - \frac{32}{5}

Passos da solução

\frac{( x - 2 ) ^{5}}{5}

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

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

Aplicar as propriedades das frações:

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

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

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

\frac{10 x ^{4}}{5} = 2 x^{4}

\frac{40 x ^{3}}{5} = 8 x^{3}

\frac{80 x ^{2}}{5} = 16 x^{2}

\frac{80 x}{5} = 16 x

= \frac{x ^{5}}{5} - 2 x^{4} + 8 x^{3} - 16 x^{2} + 16 x - \frac{32}{5}

e x p an d (x^{2} + 3 x - 1)^{7} (2 x - 3) d x

e x p an d lo g_{5} 3 \frac{( x + 9 ) ^{9}}{5}

e x p an d (cos (x) + cot (x))^{2}

s im pl i f y x (x^{2} + 2 x)

e x p an d \frac{2 - tan ( x ) + x sec ^{2} ( x )}{( 2 - tan ( x ) ) ^{2}}