展开 (x+1)^3(1-x)

解答

展开

(x + 1)^{3} (1 - x)

- x^{4} - 2 x^{3} + 2 x + 1

求解步骤

(x + 1)^{3} (1 - x)

展开

(x + 1)^{3} : x^{3} + 3 x^{2} + 3 x + 1

= (x^{3} + 3 x^{2} + 3 x + 1) (1 - x)

打开括号

= x^{3} \cdot 1 + x^{3} (- x) + 3 x^{2} \cdot 1 + 3 x^{2} (- x) + 3 x \cdot 1 + 3 x (- x) + 1 \cdot 1 + 1 \cdot (- x)

化简

x^{3} \cdot 1 + x^{3} (- x) + 3 x^{2} \cdot 1 + 3 x^{2} (- x) + 3 x \cdot 1 + 3 x (- x) + 1 \cdot 1 + 1 \cdot (- x) : - x^{4} - 2 x^{3} + 2 x + 1

= - x^{4} - 2 x^{3} + 2 x + 1

\frac{d}{d x} (5 e^{x} sin (x))

d er i v a t i v e s (t) = t^{3} - 5 t^{2} - 3 t + 8

\frac{d y}{d x} + \frac{y}{x} = 2 x^{6} y^{2}

d er i v a t i v e f (x) = x^{2} \cdot e^{- x^{2}}

f (x) = \frac{50}{x}