展开 x^{4/5}*(x-4)^2

解答

展开

x^{\frac{4}{5}} \cdot (x - 4)^{2}

x^{\frac{14}{5}} - 8 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 16

求解步骤

x^{\frac{4}{5}} (x - 4)^{2}

展开

(x - 4)^{2} : x^{2} - 8 x + 16

= x^{\frac{4}{5}} (x^{2} - 8 x + 16)

使用分配律:

m (a + b + c) = ma + mb + m c

x^{\frac{4}{5}} (x^{2} - 8 x + 16) = x^{\frac{4}{5}} x^{2} + x^{\frac{4}{5}} (- 8 x) + x^{\frac{4}{5}} \cdot 16

= x^{\frac{4}{5}} x^{2} + x^{\frac{4}{5}} (- 8 x) + x^{\frac{4}{5}} \cdot 16

x^{\frac{4}{5}} x^{2} = x^{\frac{14}{5}}

x^{\frac{4}{5}} (- 8 x) = - 8 x^{\frac{9}{5}}

= x^{\frac{14}{5}} - 8 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 16

e x p an d ∣ u - v ∣^{2}

e x p an d \frac{m}{s ( s + k )}

e x p an d \frac{2000}{( s + 1 ) ( s + 50 ) ( s + 100 )}

e x p an d (1 + \frac{x}{4})^{3}

e x p an d \frac{50 ( 1 + 0.5 t )}{2 + 0.01 t}