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受欢迎的代数 >

因式分解 81(7a+3)^4-72(7a+3)^2+16

解答

因式分解

81 (7 a + 3)^{4} - 72 (7 a + 3)^{2} + 16

解答

49 (21 a + 11)^{2} (3 a + 1)^{2}

求解步骤

81 (7 a + 3)^{4} - 72 (7 a + 3)^{2} + 16

令

u = (7 a + 3)^{2}

= 81 u^{2} - 72 u + 16

分解

81 u^{2} - 72 u + 16 : (9 u - 4) (9 u - 4)

= (9 u - 4) (9 u - 4)

u = (7 a + 3)^{2}

代回

= (9 (7 a + 3)^{2} - 4) (9 (7 a + 3)^{2} - 4)

分解

9 (7 a + 3)^{2} - 4 : (3 (7 a + 3) + 2) (3 (7 a + 3) - 2)

= (3 (7 a + 3) + 2) (3 (7 a + 3) - 2) (9 (7 a + 3)^{2} - 4)

分解

9 (7 a + 3)^{2} - 4 : (3 (7 a + 3) + 2) (3 (7 a + 3) - 2)

= (3 (7 a + 3) + 2) (3 (7 a + 3) - 2) (3 (7 a + 3) + 2) (3 (7 a + 3) - 2)

整理后得

= (3 (7 a + 3) + 2)^{2} (3 (7 a + 3) - 2)^{2}

(3 (7 a + 3) + 2)^{2} = (21 a + 11)^{2}

= (21 a + 11)^{2} (3 (7 a + 3) - 2)^{2}

(3 (7 a + 3) - 2)^{2} = 49 (3 a + 1)^{2}

= 49 (21 a + 11)^{2} (3 a + 1)^{2}

流行的例子

化简 8sqrt(7)+12sqrt(63)

s im pl i f y 87 + 1263

2 x^{2} + 10 x - 31 = 7 x

1/7+3/5 >= x/(35)

\frac{1}{7} + \frac{3}{5} \geq \frac{x}{35}

- 0.75 p - 2 = 0.25 p

∣ x + 7 ∣ + 8 = 7