因数 9a^4-a^2-12a-36

解

因数

9 a^{4} - a^{2} - 12 a - 36

(3 a^{2} + a + 6) (3 a^{2} - a - 6)

解答ステップ

9 a^{4} - a^{2} - 12 a - 36

因数

- a^{2} - 12 a - 36 : - (a + 6)^{2}

= 9 a^{4} - (a + 6)^{2}

簡素化

9 a^{4} : (3 a^{2})^{2}

= (3 a^{2})^{2} - (a + 6)^{2}

2乗の差の公式を適用する:

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

(3 a^{2})^{2} - (a + 6)^{2} = (3 a^{2} + (a + 6)) (3 a^{2} - (a + 6))

= (3 a^{2} + (a + 6)) (3 a^{2} - (a + 6))

簡素化

(3 a^{2} + (a + 6)) (3 a^{2} - (a + 6)) : (3 a^{2} + a + 6) (3 a^{2} - a - 6)

= (3 a^{2} + a + 6) (3 a^{2} - a - 6)