Question

(a2-a)2-8(a-2)(a+1)-1因式分解

(a2-a)2-8(a-2)(a+1)-1因式分解

Answer 1

a^2-a-2=(a-2)(a+1). 若是a^2-a+2,则在实数范围内不能分解因式，但能在复数范围内分解因式，即： a^2-a+2=(a-1/2)^2-1/4+2 =(a-1/2)^2+7/4. =(a-1/2)^2-(√7/2i)^2. =(a-1/2+√7/2i)(a-1/2-√7/2I)

Answer 2

(a²-a)²-8(a-2)(a+1)-1
=(a⁴-2a³+a²)-8(a²-a-2)-1
=a⁴-2a³+a²-8a²+8a+16-1
=a⁴-2a³-7a²+8a+15
=a⁴-a³-a³-3a²+a²-5a²+3a+5a+15
=a⁴-a³-3a²-a³+a²+3a-5a²+5a+15
=(a⁴-a³-3a²)-(a³-a²-3a)-(5a²-5a-15)
=a²(a²-a-3)-a(a²-a-3)-5(a²-a-3)
=(a²-a-3)(a²-a-5)

Answer 3

1:(a^2-a-3)(a^2-a-5)2:(c-2a+b)^2

Answer 4

(-5 - a + a^2) (-3 - a + a^2)