ab（c²-d²）-（a²-d²）cd

题目

ab（c²-d²）-（a²-d²）cd
x的2n次方+x的n次方-1/9y的4m次方+1/4
（1+y）²-2x²（1+y²）+x4（1-y）²
x²-y²+2x+6y-8
-14x²y²+x4+y4

答案

ab(c²-d²)-(a²-b²)cd
=abc²-abd²-a²cd+b²cd
=(abc²-a²2cd)+(b²cd-abd²)
=ac(bc-ad)+bd(bc-ad)
=(ac+bd)(bc-ad)；
x^(2n)+x^n-1/9y^(4m)+1/4
=[x^(2n)+x^n+1/4]-1/9y^(4m)
=(x^n+1/2)²-(1/3y^2m)²
=(x^n+1/2+1/3y^2m)(x^n+1/2-1/3y^2m)
(1+y)²-2x²(1+y)²+x^4(1+y)²
=(1+y)²[1-2x²+x^4]
=(1+y)²(1-x²)²
=(1+y)²(1+x)²(1-x)²
x²-y²+2x+6y-8
=( x²+2x+1)-(y²-6y+9)
=(x+1)²-(y-3)²
=(x+y-2)(x-y+4)
-14x²y²+x^4+y^4
=x^4+y^4+2x²y²-16x²y²
=(x²+y²)²-16x²y²
=(x²+y²+4xy)(x²+y²-4xy)
=[(x+2y)^2-3y^2][(x-2y)^2-3y^2]
=(x+2y+√3y)(x+2y-√3y)(x-2y+√3y)(x-2y-√3y)