4(x+2y)^2+25(x-y)^2

题目

4(x+2y)^2+25(x-y)^2
还有一个 2xy-x^2-y^2+1

答案

题目是4(x+2y)^2-25(x-y)^2吧?
4(x+2y)^2-25(x-y)^2
=[2(x+2y)+5(x-y)][2(x+2y)-5(x-y)]
=(7x-y)(-3x+9y)
2xy-x^2-y^2+1
=1-(x-y)^2
=(1+x-y)(1-x+y)