因式分解 1+1000x^6

解答

因式分解

1 + 1000 x^{6}

(10 x^{2} + 1) (100 x^{4} - 10 x^{2} + 1)

求解步骤

1 + 1000 x^{6}

改写成标准形式

= 1000 x^{6} + 1

使用指数运算法则

= (10 x^{2})^{3} + 1^{3}

使用立方和公式:

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

(10 x^{2})^{3} + 1^{3} = (10 x^{2} + 1) (1 0^{2} x^{4} - 10 x^{2} + 1)

= (10 x^{2} + 1) (1 0^{2} x^{4} - 10 x^{2} + 1)

1 0^{2} = 100

= (10 x^{2} + 1) (100 x^{4} - 10 x^{2} + 1)

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