Question

1999^2-1998^2=-x^2+4xy-4y^2=4(a-b)^2-9a+9b=1/2x^2+2xy+2y^2=

Answer 1

1999^2-1998^2=(1999+1998)(1999-1998)=3997

-x^2+4xy-4y^2= -(x^2-4xy+4y^2)=-(x-2y)^2

4(a-b)^2-9a+9b=4(a-b)^2-9(a-b)=(a-b)(4a-4b-9)

1/2x^2+2xy+2y^2=1/2(x^2+4xy+4y^2)=1/2(x+2y)^2