因式分解 343z^3+27x^3

解答

因式分解

343 z^{3} + 27 x^{3}

(7 z + 3 x) (49 z^{2} - 21 z x + 9 x^{2})

求解步骤

343 z^{3} + 27 x^{3}

使用指数运算法则

= (7 z)^{3} + (3 x)^{3}

使用立方和公式:

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

(7 z)^{3} + (3 x)^{3} = (7 z + 3 x) ((7 z)^{2} - 7 z \cdot 3 x + (3 x)^{2})

= (7 z + 3 x) ((7 z)^{2} - 7 z \cdot 3 x + (3 x)^{2})

化简

(7 z)^{2} - 7 z \cdot 3 x + (3 x)^{2} : 49 z^{2} - 21 z x + 9 x^{2}

= (7 z + 3 x) (49 z^{2} - 21 z x + 9 x^{2})

f a c t or 5 x^{2} - 21 x - 20

f a c t or 5 v^{2} - 30 v + 40

f a c t or 20 x^{2} y - 28 x

2 x - 3 (x + 3) < 14

- 4 x + 4 = 0