展开 (x-5x^2)^3

解答

展开

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

x^{3} - 15 x^{4} + 75 x^{5} - 125 x^{6}

求解步骤

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

使用完全立方公式:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

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

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

化简

x^{3} - 3 x^{2} \cdot 5 x^{2} + 3 x (5 x^{2})^{2} - (5 x^{2})^{3} : x^{3} - 15 x^{4} + 75 x^{5} - 125 x^{6}

= x^{3} - 15 x^{4} + 75 x^{5} - 125 x^{6}

s im pl i f y (\frac{( 3 x ^{5} )}{( y ^{6} )})^{0}

s im pl i f y x + 1 x + 2 x + 3 x + 4 - 15

f a c t or x^{3} + 3 x + 4

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

e x p an d 64 (3 x - 4)^{2} - 36 y^{2}