因式分解 49x^{16}-16y^{64}

解答

因式分解

49 x^{16} - 16 y^{64}

(7 x^{8} + 4 y^{32}) (7 x^{8} - 4 y^{32})

求解步骤

49 x^{16} - 16 y^{64}

49 x^{16} = (7 x^{8})^{2}

16 y^{64} = (4 y^{32})^{2}

= (7 x^{8})^{2} - (4 y^{32})^{2}

使用平方差公式:

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

(7 x^{8})^{2} - (4 y^{32})^{2} = (7 x^{8} + 4 y^{32}) (7 x^{8} - 4 y^{32})

= (7 x^{8} + 4 y^{32}) (7 x^{8} - 4 y^{32})

2 x^{2} - 3 = - 203

- 2 t - 5 < 9

f a c t or t^{2} + 24 t + 144

r - 2 > 11

7 x + 10 = - 4 x - 23