初一数学因式分解（用完全平方公式分解）

1、（a+1）(a+5)+4=
=a²+6a+5+4
=a²+6a+9
=(a+3)²

2、（m²+n²）²-4m²n²=
=(m²+n²+2mn)(m²+n²-2mn)
=(m+n)²(m-n)²

3、x²+2x+1-y²
=(x+1)²-y²
=(x+y+1)(x-y+1)

4、(a+1）²（2a-3）-2（a+1）(3-2a)+2a-3=
=(a+1）²（2a-3）+2（a+1）(2a-3)+2a-3
(2a-3)[(a+1)²+2(a+1)+1]
=(2a-3)[(a+1)+1]²
=(2a-3)(a+2)²

1. (a+1)(a+5)+4=(a+1)[(a+1)+4]+4=(a+1)^2+4(a+1)+4=(a+1+2)^2=(a+3)^2

2. (m^2+n^2)^2-4m^2n^2=(m^2+n^2+2mn)(m^2+n^2-2mn)=[(m+n)^2][(m-n)^2]=(m^2-n^2)^2

3. x^2+2x+1-y^2=(x+1)^2-y^2=(x+1+y)(x+1-y)

4. (a+1)^2(2a-3)-2(a+1)(3-2a)+2a-3=(a+1)^2(2a-3)+2(a+1)(2a-3)+(2a-3)=(2a-3)[(a+1)^2+2(a+1)+1]=(2a-3)(a+1+1)^2=(2a-3)(a+2)^2

1.a^2+6a+9=(a+3)^2 2.m^4+n^4-2m^2n^2=(m^2-n^2)^2 3.(x+1)^2-y^2=(x+y+1)(x+1-y) 4.(a+1）²（2a-3）-2（a+1）(3-2a)+2a-3=
=(a+1）²（2a-3）+2（a+1）(2a-3)+2