因式分解 64a^3-27b^3

解答

因式分解

64 a^{3} - 27 b^{3}

(4 a - 3 b) (16 a^{2} + 12 ab + 9 b^{2})

求解步骤

64 a^{3} - 27 b^{3}

使用指数运算法则

= (4 a)^{3} - (3 b)^{3}

使用立方差公式:

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

(4 a)^{3} - (3 b)^{3} = (4 a - 3 b) ((4 a)^{2} + 4 a \cdot 3 b + (3 b)^{2})

= (4 a - 3 b) ((4 a)^{2} + 4 a \cdot 3 b + (3 b)^{2})

化简

(4 a)^{2} + 4 a \cdot 3 b + (3 b)^{2} : 16 a^{2} + 12 ab + 9 b^{2}

= (4 a - 3 b) (16 a^{2} + 12 ab + 9 b^{2})

(\frac{2}{3})^{2} + (x)^{2} = 1^{2}

(x + 1) (x - 8)^{2} (x - 3) \geq 0

∣ x + 6 ∣ = ∣ 6 - x ∣

s im pl i f y i^{87}

y^{2} + \frac{7}{4} y + \frac{49}{64} = 0