因式分解 a^4-81b^4

解答

因式分解

a^{4} - 81 b^{4}

(a^{2} + 9 b^{2}) (a + 3 b) (a - 3 b)

求解步骤

a^{4} - 81 b^{4}

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

81 b^{4} = (9 b^{2})^{2}

= (a^{2})^{2} - (9 b^{2})^{2}

使用平方差公式:

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

(a^{2})^{2} - (9 b^{2})^{2} = (a^{2} + 9 b^{2}) (a^{2} - 9 b^{2})

= (a^{2} + 9 b^{2}) (a^{2} - 9 b^{2})

因式分解

a^{2} - 9 b^{2} : (a + 3 b) (a - 3 b)

= (a^{2} + 9 b^{2}) (a + 3 b) (a - 3 b)

s im pl i f y (arcsin (x))^{32} 1 - x^{2}

s im pl i f y \frac{3 x - 9}{9 - 9 x}

s im pl i f y 3^{2 + l o g_{3} (4)} j

s im pl i f y \frac{( 4 y ^{2} - 16 )}{( y ^{2} + 3 y + 2 )}

s im pl i f y - 0.4 (- 6 g - 6 h) - 2 h - 0.2 (- 5 h + 3 g)