因式分解 a^4-16b^4

解答

因式分解

a^{4} - 16 b^{4}

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

求解步骤

a^{4} - 16 b^{4}

a^{4} = (a^{2})^{2}

16 b^{4} = (4 b^{2})^{2}

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

使用平方差公式:

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

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

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

因式分解

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

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

s im pl i f y 1 - cos^{2} (a)

f a c t or x^{10} - 10 x^{6} + 9 x^{2}

e x p an d (x + 4) (x + 2) (x - 1) (x - 3)

f a c t or 27 - 125 a^{3} - 135 a + 225 a^{2}

s im pl i f y (- x + \frac{1}{5} - x^{3}) - (\frac{1}{2} x - x^{3} - \frac{4}{5})