Factorize the following expressions:

x² + 2x + 1

= x² + 2x + 1

Method 1

It is of the form a² + 2ab + b²
Where a = x and b = 1.

Using the identity: (a + b)² = a² + 2ab + b²

We get,

⇒ x² + 2x + 1 = (x + 1)²

Method 2
Here 2x can be elaborated as x + x

we get,

= x² + x + x + 1

Taking x common in x² + x

we get,

= x(x + 1) + x + 1
Taking (x + 1) common in both the terms

we get,
= (x + 1)(x + 1)
= (x + 1)²
x² + 2x + 1 = (x + 1)²