1.x^3-x=x(x^2-1)=x(x+1)(x-1)
2.(a+2b)^2+2(a^2-4b^2)+(a-2b)^2=(a+2b)^2+2(a+2b)(a-2b)+(a-2b)^2=[(a+2b)+(a-2b)]^2=(2a)^2
3.2x^4-32=2(x^4-16)=2(x^2+4)(x^2-4)=2(x^2+4)(x+2)(x-2)
4.16x^4-8x^2y^2+y^4=(4x^2-y^2)^2=(2x+y)^2(2x-y)^2
5.(a+b)x^2+2xy(a+b)+(a+b)y^2=(a+b)(x^2+2xy+y^2)=(a+b)(x+y)^2
6.x^2/2-2xy+2y^2=1/2(x^2-4xy+4y^2)=1/2(x-2y)^2
7.(x^2+4)^2-16x^2=(x^2+4x+4)(x^2-4x+4)=(x+2)^2(x-2)^2
8.4x^2-16y^2=(2x-4y)(2x+4y)=4(x-2y)(x+2y)
9.4x^2-8xy+4y=4(x^2-2xy+y)=4(x-y)^2
10.x(m-n)^2-6x(m+n)+9x=x((m+n)^2-6(m+n)+9)=x(m+n-3)^2
注：
^2表示平方
^3表示立方
^4表示四次方
依此类推