因式分解-64a^4+9b^6

解答

因式分解

- 64 a^{4} + 9 b^{6}

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

求解步骤

- 64 a^{4} + 9 b^{6}

= 9 b^{6} - 64 a^{4}

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

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

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

使用平方差公式:

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

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

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

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

s im pl i f y \frac{a}{( a - 1 ) \cdot ( a - 1 ) ^{2} + 1}

f a c t or 9 m^{4} + 14 m^{2} n^{2} + 25 n^{4}

s im pl i f y \frac{6 y ^{5} + 4 y ^{3} - 10 y ^{2} + 2 y}{2 y}

s im pl i f y sin^{2} (q) + cos^{2} (q)