展开 (x^2+2x-1)^3(5x)

解答

展开

(x^{2} + 2 x - 1)^{3} (5 x)

5 x^{7} + 30 x^{6} + 45 x^{5} - 20 x^{4} - 45 x^{3} + 30 x^{2} - 5 x

求解步骤

(x^{2} + 2 x - 1)^{3} (5 x)

去除括号:

(a) = a

= (x^{2} + 2 x - 1)^{3} \cdot 5 x

(x^{2} + 2 x - 1)^{3} = x^{6} + 6 x^{5} + 9 x^{4} - 4 x^{3} - 9 x^{2} + 6 x - 1

= 5 x (x^{6} + 6 x^{5} + 9 x^{4} - 4 x^{3} - 9 x^{2} + 6 x - 1)

= 5 x (x^{6} + 6 x^{5} + 9 x^{4} - 4 x^{3} - 9 x^{2} + 6 x - 1)

打开括号

= 5 x x^{6} + 5 x \cdot 6 x^{5} + 5 x \cdot 9 x^{4} + 5 x (- 4 x^{3}) + 5 x (- 9 x^{2}) + 5 x \cdot 6 x + 5 x (- 1)

使用加减运算法则

+ (- a) = - a

= 5 x^{6} x + 5 \cdot 6 x^{5} x + 5 \cdot 9 x^{4} x - 5 \cdot 4 x^{3} x - 5 \cdot 9 x^{2} x + 5 \cdot 6 xx - 5 \cdot 1 \cdot x

化简

5 x^{6} x + 5 \cdot 6 x^{5} x + 5 \cdot 9 x^{4} x - 5 \cdot 4 x^{3} x - 5 \cdot 9 x^{2} x + 5 \cdot 6 xx - 5 \cdot 1 \cdot x : 5 x^{7} + 30 x^{6} + 45 x^{5} - 20 x^{4} - 45 x^{3} + 30 x^{2} - 5 x

= 5 x^{7} + 30 x^{6} + 45 x^{5} - 20 x^{4} - 45 x^{3} + 30 x^{2} - 5 x

e x p an d (y e^{- x} - sin (x)) d x - (e^{- x} + 2 y) d y

e x p an d (2 x - 1) ln (5)

e x p an d \frac{4}{1.3} (e^{0, 8 x} - e^{- 0.5 x}) + 2 e^{- 0.5 x}

e x p an d (x^{2} + 6) 1 - x

e x p an d \frac{2}{( x - 2 ) ^{3}}