= 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

I didn't see what you wrote!

4.( 1/2 * X+2/3Y-3/4 Z)2-( 1/2 * X-2/3Y-3/4 Z)2

=(x/2+2y/3-3z/4)^2-(x/2-2y/3-3z/4)^2

[If (X/2-3Z/4) is proposed as an item, (a+b) 2 = a 2+2ab+b 2]

=[(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)