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受欢迎的代数 >

因式分解 a^4-2a^2+1

解答

因式分解

a^{4} - 2 a^{2} + 1

解答

(a + 1)^{2} (a - 1)^{2}

求解步骤

a^{4} - 2 a^{2} + 1

令

u = a^{2}

= u^{2} - 2 u + 1

因式分解

u^{2} - 2 u + 1 : (u - 1)^{2}

= (u - 1)^{2}

u = a^{2}

代回

= (a^{2} - 1)^{2}

因式分解

a^{2} - 1 : (a + 1) (a - 1)

= ((a + 1) (a - 1))^{2}

使用指数法则:

(a \cdot b)^{n} = a^{n} b^{n}

((a + 1) (a - 1))^{2} = (a + 1)^{2} (a - 1)^{2}

= (a + 1)^{2} (a - 1)^{2}

流行的例子

0.2(x+50)-6=0.4(3x+20)

0.2 (x + 50) - 6 = 0.4 (3 x + 20)

98 = 7 v^{2} + 42

(x + 5)^{2} = 4 x^{2}

∣ 5 + 2 x ∣ \geq 3

∣ 7 x - 5 ∣ + 5 = 8