分解因式:a^2-2ab+b^2-c^2-2c-1分解因式:1.a^2-2ab+b^2-c^2-2c-12.(X-1)(X-3)-13.(a^2-2a)^2+12a-6a^2+9

Question

分解因式:a^2-2ab+b^2-c^2-2c-1
分解因式:1.a^2-2ab+b^2-c^2-2c-1
2.(X-1)(X-3)-1
3.(a^2-2a)^2+12a-6a^2+9

Answer 1

1.a^2-2ab+b^2-c^2-2c-1
=(a-b)^2-(c+1)^2
=(a-b+c-1)(a-b-c+1)
2.(X-1)(X-3)-1
=x^2-4x+3-1
=x^2-4x+2
有理数范围内无法分解
.(X-1)(X-3)+1
=x^2-4x+3+1
=x^2-4x+4
=(x-2)^2
3.(a^2-2a)^2+12a-6a^2+9
=a^2(a-2)^2-6a(a-2)+9
=(a(a-2)-3)^2
=(a^2-2a-3)^2
=(a-3)^2(a+1)^2