28.
a, ( x+y )² - ( x-y )² = x² + 2xy + y² - x² - 2xy + y²
= 2y²
b, ( 3x+1 )² - ( x+1 )² = (3x)² + 2.3x + 1² - x² + 2x + 1²
= 9x² + 6x + 1 - x² + 2x + 1
= 8x² + 8x + 2 = 2( 4x² + 4x + 1 )
c, x³ + y³ + z³ - 3xyz = [ ( x + y )³ + z³ ] - 3xyz
= ( x+ y )³ + 3.(x+y)².z + 3.(x+y).z² - z³ - 3xyz
= x³ + 3x²y + 3xy²+y³ + 3xz² + 3yz² - 3xyz
= x³ + 3x²y + 3xy² + y³ + 3xz² + 3yz² - 3xyz
= (x+y)³ + 3z.( xz + yz + xy )