Question

factorise:  x² + 6x + 9 - 4y² 

Answer 1

x² + 6x + 9 - 4y² 

= (x)² + 2 × x × 3 + (3)² - (2y)²

             ...[(a + b)² = a² + 2ab + b²]
             ...[a² - b² = (a + b)(a - b)]   

= (x + 3)² - (2y)²

= (x + 3 + 2y) (x + 3 - 2y)

= (x + 2y + 3) (x - 2y + 3)