1、25(X+Y)^2-16(X-Y)^2
= 25(X^2+2XY+Y^2)-16(X^2-2XY+Y^2)
=25X^2-16X^2+50XY+32XY+25Y^2-16Y^2
=9X^2-82XY+9Y^2
=(9X-Y)(X-9Y)
2、(X+Y)^2-14Y(X+Y)+49Y^2
=X^2+Y^2+2XY-14XY-14Y^2+49Y^2
=X^2-12XY+36Y^2
=(X-6Y)^2
3、没看清你写的是什么!
4、(二分之一*X+三分之二Y-四分之三Z)^2-(2分之一*X-三分之2Y-四分之三*Z)^2
=(X/2+2Y/3-3Z/4)^2-(X/2-2Y/3-3Z/4)^2
[把(X/2-3Z/4)提出来看作一项,就可以用（A+B）^2 = A^2+2AB+B^2了]
=[(X/2-3Z/4)+2Y/3]^2-[(X/2-3Z/4)-2Y/3]^2
=(X/2-3Z/4)^2+2(X/2-3Z/4)(2Y/3)+(2Y/3)^2-(X/2-3Z/4)^2+2(X/2-3Z/4)(2Y/3)-(2Y/3)^2
=4(X/2-3Z/4)(2Y/3)
=(2X-3Z)(2Y/3)