Question

因式分解1.m²-2mn+n²-4m+4n-5 2.x^4+x²y²+y^4 3.(x²+x-4)(x²+x+3)+10

附加题（做出再加10分）
因式分解x²-xy-6y²-x+8y-2

Answer 1

1.    m²-2mn+n²-4m+4n-5

   =(m²-2mn+n²)-4(m-n)-5

   =(m-n)²-4(m-n)-5

   =[(m-n)+1][(m-n)-5]

   =(m-n+1)(m-n-5)

2. x^4+x²y²+y^4

   =（x²+y²）²-x²y²

   =(x²+y²+xy)(x²+y²-xy)

3. (x²+x-4)(x²+x+3)+10

   =(x²+x)²-(x²+x)-12+10

   =(x²+x)²-(x²+x)-2

   =[(x²+x)+1][(x²+x)-2]

   =(x²+x+1)(x²+x-2)

 

Answer 2

1、m²-2mn+n²-4m+4n-5
=（m-n)^2-4(m-n)-5
=(m-n-5)(m-n+1)

2、x^4+x²y²+y^4
=(x^2+y^2)^2-x²y²
=(x^2+y^2-xy)(x^2+y^2+xy)

3、(x²+x-4)(x²+x+3)+10
=(x²+x)^2-(x²+x)-12+10
=(x²+x)^2-(x²+x)-2
=(x²+x-2)(x²+x+1)
=(x+2)(x-1)(x²+x+1)

4、x²-xy-6y²-x+8y-2
=x²-x(y+1)-(6y²-8y+2)
=x²-x(y+1)-(3y-1)(2y-2)
=(x-3y+1)(x+2y-2)