展开 20x(x+9)^4dx

解答

展开

20 x (x + 9)^{4} d x

20 x^{5} d x + 720 x^{4} d x + 9720 x^{3} d x + 58320 x^{2} d x + 131220 x d x

求解步骤

20 x (x + 9)^{4} d x

(x + 9)^{4} = x^{4} + 36 x^{3} + 486 x^{2} + 2916 x + 6561

= 20 x (x^{4} + 36 x^{3} + 486 x^{2} + 2916 x + 6561) d x

打开括号

= 20 x d x x^{4} + 20 x d x \cdot 36 x^{3} + 20 x d x \cdot 486 x^{2} + 20 x d x \cdot 2916 x + 20 x d x \cdot 6561

= 20 x^{4} x d x + 20 \cdot 36 x^{3} x d x + 20 \cdot 486 x^{2} x d x + 20 \cdot 2916 xx d x + 20 \cdot 6561 x d x

化简

20 x^{4} x d x + 20 \cdot 36 x^{3} x d x + 20 \cdot 486 x^{2} x d x + 20 \cdot 2916 xx d x + 20 \cdot 6561 x d x : 20 x^{5} d x + 720 x^{4} d x + 9720 x^{3} d x + 58320 x^{2} d x + 131220 x d x

= 20 x^{5} d x + 720 x^{4} d x + 9720 x^{3} d x + 58320 x^{2} d x + 131220 x d x

e x p an d \frac{700}{( p + 8 ) ^{4}}

e x p an d \frac{( 2 x - 4 + 3 ) ( x - 2 )}{3}

s im pl i f y (1 - 3 x + 2)^{2}

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

e x p an d \frac{8 s ( s + 1 ) ( s - 6 )}{( s + 2 ) ( s + 3 ) ( s - 7 )}