因式分解 1000x^3y^3-z^3

解答

因式分解

1000 x^{3} y^{3} - z^{3}

(10 x y - z) (100 x^{2} y^{2} + 10 x yz + z^{2})

求解步骤

1000 x^{3} y^{3} - z^{3}

将

1000 x^{3} y^{3}

改写为

(10 x y)^{3}

= (10 x y)^{3} - z^{3}

使用立方差公式:

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

(10 x y)^{3} - z^{3} = (10 x y - z) ((10 x y)^{2} + 10 x yz + z^{2})

= (10 x y - z) ((10 x y)^{2} + z 10 x y + z^{2})

化简

(10 x y - z) ((10 x y)^{2} + 10 x yz + z^{2}) : (10 x y - z) (100 x^{2} y^{2} + 10 x yz + z^{2})

= (10 x y - z) (100 x^{2} y^{2} + 10 x yz + z^{2})

f a c t or m^{18} y^{3} - n^{3} z^{18}

f a c t or (x + 2 y)^{3} + 1

f a c t or x^{3} - 6 x - 5 x + 30

f a c t or x (2 y)

f (x) = (sin (2 x))^{4}