因式分解 a^8-b^8

解答

因式分解

a^{8} - b^{8}

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

求解步骤

a^{8} - b^{8}

a^{8} = (a^{4})^{2}

b^{8} = (b^{4})^{2}

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

使用平方差公式:

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

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

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

因式分解

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

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

5 x^{2} + 9 = 4 x + 5

3 (k - 2) - 6 = 4 k - (3 k - 1)

s im pl i f y - (\frac{2}{3})^{3}

4 x + 6 + x < 4 + 3 x - 4

s im pl i f y \frac{x ^{5} y ^{2}}{x y ^{2}}