Factorise :

a² + 2ab + b² - c²

a² + 2ab + b² - c²

Using the formula

[∵ (x + y)² = x² + y² + 2xy]

= (a² + 2ab + b²) - c²

= ((a)² + 2 $\times$ a $\times$ b + (b)²) - c²

= (a + b)² - (c)²

Using the formula

[∵ (x² - y²) = (x + y)(x - y)]

= ((a + b) + c)((a + b) - c)

= (a + b + c)(a + b - c)

Hence,a² + 2ab + b² - c² = (a + b + c)(a + b - c)