因式分解 64a^6-b^6

解答

因式分解

64 a^{6} - b^{6}

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

求解步骤

64 a^{6} - b^{6}

64 a^{6} = (8 a^{3})^{2}

b^{6} = (b^{3})^{2}

= (8 a^{3})^{2} - (b^{3})^{2}

使用平方差公式:

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

(8 a^{3})^{2} - (b^{3})^{2} = (8 a^{3} + b^{3}) (8 a^{3} - b^{3})

= (8 a^{3} + b^{3}) (8 a^{3} - b^{3})

因式分解

8 a^{3} + b^{3} : (2 a + b) (4 a^{2} - 2 ab + b^{2})

= (2 a + b) (4 a^{2} - 2 ab + b^{2}) (8 a^{3} - b^{3})

因式分解

8 a^{3} - b^{3} : (2 a - b) (4 a^{2} + 2 ab + b^{2})

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

s im pl i f y \frac{( a ^{8} a ^{6} ) ^{\frac{1}{7}}}{a ^{2}}

f a c t or 1 - 64 a^{3} - 12 a + 48 a^{2}

e x p an d (a + 7)^{3}

s im pl i f y \frac{( 5 x ^{2} - 33 x - 14 )}{( x ^{2} - 7 x )}

e x p an d (a - 6)^{3}