a)$(x-y)^{2}$ + $2(x+y)^{2}$ - $(x-y)(x+y)$
= $x² - 2xy + y² + 2(x² +2xy + y² ) - (x² - y²)$
= $x² - 2xy + y² + 2x² +4xy + 2y² - x² + y²$
= $2x² +2xy + 4y²$ = $2(x² +2xy + 2y²)$
b) $(x-1)² - 2(x-1)(x-3) + (x-3)²$
$= [(x-1) - (x-3)]²$ = $= (x-1 - x+3)²$ = 2² =4
c) $(x+1)² + 2(x+1)(3y-1) + (1- 3y)²$
$= (x+1)² + 2(x+1)(3y-1) + (3y-1)²$
$=[(x+1) + (3y-1)]²$ $= (x+1 + 3y-1)²$ $= (x+3y)²$
d)$(5x-2)² +4(5x-2)(1+3y) + (6y+2)²$
$= (5x-2)² +2(5x-2)(6y+2) + (6y+2)²$
$ = [(5x-2) + (6y+2)]²$ $ = (5x-2 + 6y+2)²$ = $(5x+6y)²$
e) $(x-y)² +2(x²-y²) + (x+y)²$
$= (x-y)² + 2(x-y)(x+y) + (x+y)²$
$ = [(x-y) + (x+y)]² = (x-y+x+y)² = (2x)² = 4x² $
$=(x-y)² +2(x-y)(x+y) + (x+y)²$
$ = [(x-y) + (x+y)]² = (x-y + x+y)² = (2x)² = 4x²$
