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受欢迎的代数 >

因式分解 x^9-x^6-x^3+1

解答

因式分解

x^{9} - x^{6} - x^{3} + 1

解答

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

求解步骤

x^{9} - x^{6} - x^{3} + 1

= (x^{9} - x^{6}) + (- x^{3} + 1)

从

x^{9} - x^{6}

分解出因式

x^{6}

:

x^{6} (x^{3} - 1)

从

- x^{3} + 1

分解出因式

- 1

:

- (x^{3} - 1)

= x^{6} (x^{3} - 1) - (x^{3} - 1)

因式分解出通项

(x^{3} - 1) : (x^{3} - 1) (x^{6} - 1)

= (x^{3} - 1) (x^{6} - 1)

因式分解

x^{3} - 1 : (x - 1) (x^{2} + x + 1)

= (x - 1) (x^{2} + x + 1) (x^{6} - 1)

因式分解

x^{6} - 1 : (x + 1) (x - 1) (x^{2} + 1 + x) (x^{2} + 1 - x)

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

使用指数法则:

aa = a^{2}

(x - 1) (x - 1) = (x - 1)^{2}

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

化简

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

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

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

流行的例子

1 = \frac{1}{5} (x - 25)

5 (2 x + 1) = 6 x + 13

e^{2} x - 9 e x + 20 = 0

化简-(16/21)/((-8/3))

s im pl i f y - \frac{\frac{16}{21}}{( - \frac{8}{3} )}

s im pl i f y - (\frac{1}{3})^{0}