a) (x + 2)² - (x - 2)²
= (x² + 4x + 4) - (x² - 4x + 4)
= x² + 4x + 4 - x² + 4x - 4
= 8x
b) (x - 3)² - (x + 2)²
= (x² - 6x + 9) - (x²+ 4x + 4)
= x² - 6x + 9 - x² - 4x - 4
= -10x + 5
c) (x - 4)(x² + 4x + 16) - x.(x² - 3)
= (x)³ - (4)³ - (x³ - 3x)
= x³ - 64 - x³ + 3x
= 3x - 64
d) (x + 3)(x² - 3x + 9) - x(x² + 2)
= (x)³ + (3)³ - (x³ + 2x)
= x³ + 27 - x³ - 2x
= -2x + 27
e) (x + 5)(x - 7) - (x -2)²
= (x² - 7x + 5x - 35) - (x² - 4x + 4)
= x² - 7x + 5x - 35 - x² + 4x - 4
= 2x - 39
g) (x + y)² + 2(x - y)(x + y) + (x - y)²
= [(x + y) + (x - y)]²
= (x + y + x - y)²
= (2x)²
= 4x²