展开 (4x^3+5)*(x^4+5x)^{1/2}

解答

展开

(4 x^{3} + 5) \cdot (x^{4} + 5 x)^{\frac{1}{2}}

(x^{4} + 5 x)^{\frac{1}{2}} \cdot 4 x^{3} + (x^{4} + 5 x)^{\frac{1}{2}} \cdot 5

求解步骤

(4 x^{3} + 5) (x^{4} + 5 x)^{\frac{1}{2}}

= (x^{4} + 5 x)^{\frac{1}{2}} (4 x^{3} + 5)

使用分配律:

a (b + c) = ab + a c

(x^{4} + 5 x)^{\frac{1}{2}} (4 x^{3} + 5) = (x^{4} + 5 x)^{\frac{1}{2}} \cdot 4 x^{3} + (x^{4} + 5 x)^{\frac{1}{2}} \cdot 5

= (x^{4} + 5 x)^{\frac{1}{2}} \cdot 4 x^{3} + (x^{4} + 5 x)^{\frac{1}{2}} \cdot 5

e x p an d ((X - 4) X - 1) \cdot (53 + 5 X - 1)

e x p an d \frac{( 1 + 3 j ) ( 1 + 7 j )}{( 7 - 9 j ) ( 2 - j )}

s im pl i f y (x - \frac{1}{2}) (x - 1)

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

e x p an d (1 + cot (\frac{5 π}{18})) l e f t (1 + tan (\frac{π}{36}))