x（a-x）(a-y)-y(x-a)(y-a)=(x-y)(x-a)(y-a)
-ab(a-b)^2+a(b-a)^2=(a-b)^2(-ab+a)=a(a-b)^2(1-b)
a^3b-ab=ab(a^2-1`)=ab(a+1)(a-1)
2ab^3-2ab=2ab(b^2-1)=2ab(b+1)(b-1)
1-a^4=(1-a^2)(1+a^2)=(1-a)(1+a)(1+a^2)
a^n*b^2n-a^n*c^2=a^n(b^2b-c^2)=a^n(b^n+c)(b^n-c)
m^2(x-y)+n^2(y-x)=(m^-n^2)(x-y)=(m+n)(m-n)(x-y)
a^2(b-1)-b+1=(a^2-1)(b-1)=(a+1)(a-1)(b-1)
(x^2+y^2)^2-x^2*y^2=(x^2+y^2+xy)(x^2+y^2-xy)
(2x+y)^2-(x+2y)^2 =(2x+y-x-2y)(2x+y+x+2y)=3(x-y)(x+y)
0.49P^2-144q^2=(0.7p-12q)(0.7p+12q)
81a^4-b^4=(9a^2-b^2)(9a^2+b^2)=(3a-b)(3a+b)(9a^2+b^2)
1/16M^4-1=(1/4m^2-1)(1/4m^2+1)=(1/2m-1)(1/2m+1)(1/4m^2+1)
16x^2-(x^2-y^2)^2=(4x^2-x^2+y^2)(4x^2+x^2-y^2)
=(3x^2+y^2)(√5x+y)(√5x-y)
(3m+2n)^2-(m-n)^2 =(3m+2n-m+n)(3m+2n+m-n)=(2m+3n)(4m+n)
4(x+y)^2-9(x-y)^2 =(2x+2y-3x+3y)(2x+2y+3x-3y)=(5y-x)(5y-y)
4(2p+3q)^2-(3p-q)^2=(4p+6q-3p+q)(4p+6q+3p-q)=(p+7q)(7p+5q)
(a+2b)^2-(x-3y)^2=(a+2b-x+3y)(a+2b+x-3y)
1/3m^2-3n^2=(√3m/3-√3n)(√3m/3+√3n)
a^4*x^n+3-x^n-1=x^n-1(a^4x^4-1)=x^n-1(a^2x^2+1)(ax+1)(ax-1)
27(x+y+z)^2-3(x-y-z)^2
=(3√3(x+y+z)-√3(x-y-z))(3√3(x+y+z)+√3(x-y-z))
=(2√3x+4√3y+4√3z)(4√3x+2√3y+2√3z)
=4(√3x+2√3y+2√3z)(2√3x+2√3y+√3z)