1、8X^3+4X^2-2X-1
=4X^2(2X+1)-(2X+1)
=(2X+1)(4X^2-1)
=(2X+1)(2X+1)(2X-1)
=(2X+1)^2(2X-1)
注：^后的数字表示次方.
2、4a^2-20ab+25b^2-36
=(2a)^2-2*2a*5b+(5b)^2-36
=(2a-5b)^2-6^2
=(2a-5b+6)(2a-5b-6)
3、(a^4b+a^3b^2)-a^2b^3-ab^4
=a^3b(a+b)-(a^2b^3+ab^4)
=a^3b(a+b)-ab^3(a+b)
=(a+b)(a^3b-ab^3)
=(a+b)ab(a^2-b^2)
=ab(a+b)(a+b)(a-b)
=ab(a+b)^2(a-b)
4、X^2(X+1)-Y（XY+X）
=X^3+X^2-XY^2-XY
=(X^3-XY^2)+(X^2-XY)
=X(X^2-Y^2)+X(X-Y)
=X(X+Y)(X-Y)+X(X-Y)
=X(X-Y)(X+Y+1)