a) 4c³ - 32 = 4(c³ - 8) = 4 (c - 2)(c² + 2c + 4)
b) 9x² - 6xy + y² + 12x - 4y = (9x² - 6xy + y²) + (12x - 4y) = (3x - y)² + 4(3x - y)
= (3x - y)(3x - y + 4)
c) m² + n² + 2mn + 2m + 2n + 1 =(m² + 2mn + n²) + (2m + 2n) + 1 = (m + n)² + 2(m + n) + 1= (m + n + 1)²