因式分解 343z^9-216x^6y^3

解答

因式分解

343 z^{9} - 216 x^{6} y^{3}

(7 z^{3} - 6 x^{2} y) (49 z^{6} + 42 z^{3} x^{2} y + 36 x^{4} y^{2})

求解步骤

343 z^{9} - 216 x^{6} y^{3}

将

343 z^{9}

改写为

(7 z^{3})^{3}

将

216 x^{6} y^{3}

改写为

(6 x^{2} y)^{3}

= (7 z^{3})^{3} - (6 x^{2} y)^{3}

使用立方差公式:

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

(7 z^{3})^{3} - (6 x^{2} y)^{3} = (7 z^{3} - 6 x^{2} y) ((7 z^{3})^{2} + 7 z^{3} 6 x^{2} y + (6 x^{2} y)^{2})

= (7 z^{3} - 6 x^{2} y) ((7 z^{3})^{2} + 7 z^{3} 6 x^{2} y + (6 x^{2} y)^{2})

化简

(7 z^{3} - 6 x^{2} y) ((7 z^{3})^{2} + 7 z^{3} \cdot 6 x^{2} y + (6 x^{2} y)^{2}) : (7 z^{3} - 6 x^{2} y) (49 z^{6} + 42 z^{3} x^{2} y + 36 x^{4} y^{2})

= (7 z^{3} - 6 x^{2} y) (49 z^{6} + 42 z^{3} x^{2} y + 36 x^{4} y^{2})

f a c t or 71 - 31 C e^{- K (4)}

f (x) = (cos (x^{2}))^{100}

f a c t or 100 x^{3} + 201 x^{2} + 102 + 1

f a c t or x^{2} y + x y + z x + z

f a c t or 5 m z - 30 mh - 3 n z + 18 nh