因式分解 512x^3-729y^3

解答

因式分解

512 x^{3} - 729 y^{3}

(8 x - 9 y) (64 x^{2} + 72 x y + 81 y^{2})

求解步骤

512 x^{3} - 729 y^{3}

使用指数运算法则

= (8 x)^{3} - (9 y)^{3}

使用立方差公式:

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

(8 x)^{3} - (9 y)^{3} = (8 x - 9 y) ((8 x)^{2} + 8 x \cdot 9 y + (9 y)^{2})

= (8 x - 9 y) ((8 x)^{2} + 8 x \cdot 9 y + (9 y)^{2})

化简

(8 x)^{2} + 8 x \cdot 9 y + (9 y)^{2} : 64 x^{2} + 72 x y + 81 y^{2}

= (8 x - 9 y) (64 x^{2} + 72 x y + 81 y^{2})

s im pl i f y - 38 - 200

s im pl i f y \frac{- 8 - 9 i}{- 4 i}

f a c t or p^{2} - 6 - q \cdot (p^{2} - 6) 2

5 x^{2} + 9 x = 18

- 13 \leq - 5 r + 2