因式分解 x^{10}-y^{10}

解答

因式分解

x^{10} - y^{10}

(x + y) (x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4}) (x - y) (x^{4} + x^{3} y + x^{2} y^{2} + x y^{3} + y^{4})

求解步骤

x^{10} - y^{10}

x^{10} = (x^{5})^{2}

y^{10} = (y^{5})^{2}

= (x^{5})^{2} - (y^{5})^{2}

使用平方差公式:

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

(x^{5})^{2} - (y^{5})^{2} = (x^{5} + y^{5}) (x^{5} - y^{5})

= (x^{5} + y^{5}) (x^{5} - y^{5})

因式分解

x^{5} + y^{5} : (x + y) (x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4})

= (x + y) (x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4}) (x^{5} - y^{5})

因式分解

x^{5} - y^{5} : (x - y) (x^{4} + x^{3} y + x^{2} y^{2} + x y^{3} + y^{4})

= (x + y) (x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4}) (x - y) (x^{4} + x^{3} y + x^{2} y^{2} + x y^{3} + y^{4})

f a c t or 242 h^{2} - 200

- 2 x^{2} - 9 x = - 4

s im pl i f y \frac{1.1 - 2}{( 1.1 - 1 ) ^{2}}

f a c t or 2 n^{2} + 8 n

4 - 3 (3 - n) \leq 3 (2 - 5 n)