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受欢迎的代数 >

因式分解 x^{24}-1

解答

因式分解

x^{24} - 1

解答

(x^{4} + 1) (x^{2} + 1) (x + 1) (x - 1) (x^{2} + x + 1) (x^{2} - x + 1) (x^{4} - x^{2} + 1) (x^{8} - x^{4} + 1)

求解步骤

x^{24} - 1

使用指数运算法则

= (x^{8})^{3} - 1^{3}

使用立方差公式:

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

(x^{8})^{3} - 1^{3} = (x^{8} - 1) (x^{16} + x^{8} + 1)

= (x^{8} - 1) (x^{16} + x^{8} + 1)

因式分解

x^{8} - 1 : (x^{4} + 1) (x^{2} + 1) (x + 1) (x - 1)

= (x^{4} + 1) (x^{2} + 1) (x + 1) (x - 1) (x^{16} + x^{8} + 1)

因式分解

x^{16} + x^{8} + 1 : (x^{2} + 1 + x) (x^{2} + 1 - x) (x^{4} + 1 - x^{2}) (x^{8} + 1 - x^{4})

= (x^{4} + 1) (x^{2} + 1) (x + 1) (x - 1) (x^{2} + 1 + x) (x^{2} + 1 - x) (x^{4} + 1 - x^{2}) (x^{8} + 1 - x^{4})

= (x^{4} + 1) (x^{2} + 1) (x + 1) (x - 1) (x^{2} + x + 1) (x^{2} - x + 1) (x^{4} - x^{2} + 1) (x^{8} - x^{4} + 1)

流行的例子

化简 7/100*10/3*20/7

s im pl i f y \frac{7}{100} \cdot \frac{10}{3} \cdot \frac{20}{7}

36 - x^{2} = 0

因式分解 3x^2y-48y

f a c t or 3 x^{2} y - 48 y

- 5 (5 + x) > - 10

15 = x 3