a) 3x(x - 2y) + 6y(2y - x)
= 3x(x - 2y) - 6y(x - 2y)
= (x - 2y)(3x - 6y)
= (x - 2y)(x - 2y)3
= 3(x - 2y)²
b) (b - 2c)(a - b) - (a + b)(2c - b)
= (b - 2c)(a - b) + (a + b)(b - 2c)
= (b - 2c)(a - b + a + b)
= 2a(b - 2c)
c) x²(x + 2y)² - x - 2y
= x²(x + 2y)² - (x + 2y)
= (x + 2y)[x²(x + 2y) - 1]
= (x + 2y)(x³ + 2x²y - 1)
d) 3x² - 3y² - 2(x - y)²
= 3(x² - y²) - 2(x - y)²
= 3(x - y)(x + y) - 2(x - y)²
= (x - y)[3(x + y) - 2(x - y)]
= (x - y)(3x + 3y - 2x + 2y)
= (x - y)(x + 5y)
