因式分解 a^{16}-b^{16}

解答

因式分解

a^{16} - b^{16}

(a^{8} + b^{8}) (a^{4} + b^{4}) (a^{2} + b^{2}) (a + b) (a - b)

求解步骤

a^{16} - b^{16}

a^{16} = (a^{8})^{2}

b^{16} = (b^{8})^{2}

= (a^{8})^{2} - (b^{8})^{2}

使用平方差公式:

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

(a^{8})^{2} - (b^{8})^{2} = (a^{8} + b^{8}) (a^{8} - b^{8})

= (a^{8} + b^{8}) (a^{8} - b^{8})

因式分解

a^{8} - b^{8} : (a^{4} + b^{4}) (a^{2} + b^{2}) (a + b) (a - b)

= (a^{8} + b^{8}) (a^{4} + b^{4}) (a^{2} + b^{2}) (a + b) (a - b)

s im pl i f y x^{4} y^{2} + (7 + 5) x^{2} y + 35

f a c t or d^{4} + 18 d^{2} + 81

s im pl i f y \frac{1}{( 1 + x ^{a + b} )} + \frac{1}{( 1 + x ^{b - a} )}

s im pl i f y (\frac{3}{x + 4 x}) (\frac{- 2 x - 7}{x})

s im pl i f y 3 x^{2.5} \cdot 3 x^{2.5} \cdot 3 x^{2.5} \cdot 3 x^{2.5}