a)
4x² + 4x + y² = (2x)² + 2.2x.y + y² = (2x + y)²
b)
9x² - 30x + 25y² = (3x)² - 2.3x.5y + (5y)² = (3x - 5y)²
c)
4y² - x² = (2y)² - x² = (2y - x)(2y + x)
d)
x² - 9 = x² - 3² = (x - 3)(x + 3)
e)
8x³ - 12x² + 6x - 1 = (2x)³ - 3.(2x)².1 + 3.2x.1² - 1³ = (2x - 1)³
f)
1 - 6x + 12x² - 8x³ = 1³ - 3.2x.1² + 3.(2x)².1 - (2x)³ = (1 - 2x)³
g)
x³ + 3x² + 3x + 1 = x³ + 3.x².1 + 3.x.1² + 1³ = (x + 1)³
h)
8x³ + y³ = (2x)³ + y³ = (2x + y)[(2x)²- 2x.y + y²] = (2x + y)(4x² - 2x.y + y²)
i)
27 - x³ = 3³ - y³ = (3 - x)(3² + 3.x + x²) = (3 - x)(9 + 3.x + x²)
j)
8x³ - y³ = (2x)³ - y³ = (2x - y)[(2x)² + 2x.y + y²] = (2x - y)(4x² + 2x.y + y²)
