a) (x + 1)(x² + x + 1) - (x + 7)(x² - 2)
= x³ + x² + x + x² + x + 1 - x³ + 2x - 6x² + 14
= -4x² + 4x + 15
b) (2x - 7)² - 2(7 - 2x)(5x + 7) + (5x + 7)²
= (2x - 7)² + 2(2x - 7)(5x + 7) + (5x + 7)²
= (2x - 7 + 5x + 7)²
= (7x)²
= 49x²
c) (x + 2)(x² - 2x + 4) - (1 - x)(1 + x + x²)
= (x³ + 2³) - (1 - x³)
= x³ + 8 - 1 + x³
= 2x³ + 7
d) (3x - 2)(3x + 2) - 9x(x + 1)
= (3x)² - 2² - 9x² - 9x
= 9x² - 4 - 9x² - 9x
= -9x - 4
e) (2x - 3)(4x² + 6x + 9) - x(8x² + x + 1)
= (2x)³ - 3³ - 8x³ - x² - x
= 8x³ - 27 - 8x³ - x² - x
= -x² - x - 27