因式分解 x^{12}+6x^8+12x^4+8

解答

因式分解

x^{12} + 6 x^{8} + 12 x^{4} + 8

(x^{4} + 2)^{3}

求解步骤

x^{12} + 6 x^{8} + 12 x^{4} + 8

令

u = x^{2}

= u^{6} + 6 u^{4} + 12 u^{2} + 8

分解

u^{6} + 6 u^{4} + 12 u^{2} + 8 : (u^{2} + 2) (u^{2} + 2) (u^{2} + 2)

= (u^{2} + 2) (u^{2} + 2) (u^{2} + 2)

u = x^{2}

代回

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

整理后得

= (x^{4} + 2)^{3}

f a c t or (x + 3)^{3} + 8 x^{3}

f a c t or e^{2 x} - 25

f a c t or cos^{8} (x) - 2 cos^{4} (x) + 1

f (x) = (sin (8 x))^{4}

f a c t or x - (x - y)