a) A = (2x - y)² = (2x - y)(2x - y)
= 4x² - 2xy - 2xy + y²
= 4x² - 4xy + y²
b) B = (2x - 1)² - 2(4x² - 1) + (2x + 1)²
= (2x - 1)(2x - 1) - 2(4x² - 1) + (2x + 1)(2x + 1)
= 4x² - 4x + 1 - 8x² + 2 + 4x² + 4x + 1
= -4x² + 9
c) C = -3x(x + 2)² + (x + 3)(x - 1)(x + 1) - (2x - 3)²
= -3x(x² + 4x + 4) + (x + 3)(x² - 1) - (2x - 3)(2x - 3)
= -3x³ - 12x² - 12x + x³ + 2x² - x - 3x² + 3 + 4x² - 12x + 9
= -2x³ - 19x² - 25x + 12
d) D = (6x + 1)² + (6x - 1)² - 2(1 + 6x)(6x - 1)
= (6x + 1)(6x + 1) + (6x - 1)(6x - 1) - 2(1 + 6x)(6x - 1)
= 36x² + 12x + 1 + 36x² - 12x + 1 - 12x - 2 - 72x² + 12x
= 36x² - 72x² + 36x² + 12x - 12x - 12x + 1 + 1 - 2
= 36x² - 36
e) E = (2x - 1)² - 3(x - 1)(x + 2)- (x - 3)²
= (2x - 1)(2x - 1) - 3(x² + 2x - x - 2) - (x - 3)(x - 3)
= 4x² - 4x + 1 - 3x² - 6x + 3 - x² + 6x - 9
= 4x² - 3x² - x² - 4x + 6x - 6x + 1 + 3 - 9
= 0
f) F = (x + 3)² + (x - 2)² - 2(x + 3)(x - 2)
= (x + 3)(x + 3) + (x - 2)(x - 2) - 2(x² + 3x - 2x - 6)
= x² + 6x + 9 + x² - 4x + 4 - 2x² - 6x + 12
= x² - 2x² + x² + 6x - 4x - 6x + 9 + 4 + 12
= 0