Question

y^2-9(x+y)^2.a(x-y)-b(y-x)+c(x-y)..x（m+n)-y(n+m)+(m+n)..(x+y

Answer 1

(1) y^2--9(x+y)^2=[y+3(x+y)][y--3(x+y)]

=(y+3x+3y)(y--3x--3y)

=(3x+4y)(-3x--2y)

=--(3x+4y)(3x+2y).

(2) a(x--y)--b(y--x)+c(x--y)=(x--y)((a+b+c).

(3) x(m+n)--y(m+n)+(m+n)=(m+n)(x--y+1).

(4) (x+y)^2--16(t--x)^2=[(x+y)+4(y--x)][(x+y)--4(y--x)]

=(x+y+4y--4x)(x+y--4y+4x)

=(5y--3x)(5x--3y).