运用平方差公差,完全平方公式计算计算：（x+y-2)(x+y+3）(2x+y-3)(2x-y+3)

题目

运用平方差公差,完全平方公式计算计算：（x+y-2)(x+y+3）(2x+y-3)(2x-y+3)

答案

（x+y-2)(x+y+3）=[(x+y)-2][(x+y)+3]=(x+y)^2+(3-2)(x+y)-6=(x+y)^2+(x+y)-6=x^2+2xy+y^2+x+y-6(2x+y-3)(2x-y+3) =[2x+(y-3)][2x-(y+3)]=(2x)^2-(y+3)^2=4x^2-y^2-6y-9