2. a) (c-3)c + (c-1)(c+2) = (c-3)c + (c²+2c-c-2) == (c-3)c + (c²+c-2) = c² - 3c + c² + c - 2 = 2c² - 2c - 2 = c² - c - 1
b) 32xy + 4(4x-y)² = 32xy + 4(16x² - 8xy + y²) = 32xy + 64x² - 32xy + 4y² = 64x² + 4y² = (8x-2y)(8x+2y)
3. 64a² - 81c² = (8a - 9c)(8a + 9c)
a⁸ - 12a⁹ = a⁸(1-12a)
4 - 4a³ + a⁶ = a⁶ - 4a³ + 4 = a³(a³ - 4) + 4 = (a³ - 2)²
4. 4x² - (x+2)² = (2x+x+2)(2x-x-2) = (3x+2)(x-2)
1 - 27a³ = 1³ - (3a)³ = (1 - 3a)(1 + 3a + 9a²)
c⁶ - 64a⁴ = (c³)² - (8a²)² = (c³ - 8a²)(c³ + 8a²)
a² + 4y - y² - 4a = a² - 4a + 4y - y² = a(a-4) + y(4-y) = (a-y)(a+y-4)