## Factoring the Quadratic Expression: (x+2)^2 + 5(x+2) + 4

This article will explore the process of factoring the quadratic expression: **(x+2)^2 + 5(x+2) + 4**. We will use a technique known as **substitution** to simplify the expression and make it easier to factor.

### Substitution Method

**Identify the Repeated Term:**Observe that the expression contains the term**(x+2)**repeated multiple times.**Introduce a Substitute:**Let's substitute**y = (x+2)**. This will simplify our expression.**Rewrite the Expression:**Now, our expression becomes:**y^2 + 5y + 4**.

### Factoring the Simplified Expression

The simplified expression is now a standard quadratic equation in terms of 'y'. We can factor this expression using the following steps:

**Find Two Numbers:**We need to find two numbers that:**Multiply to give 4 (the constant term).****Add up to give 5 (the coefficient of the 'y' term).**

**Identify the Numbers:**The two numbers that satisfy these conditions are**4 and 1**.**Factor the Expression:**We can now factor the expression as:**(y + 4)(y + 1)**.

### Back Substitution

**Replace 'y' with (x+2):**Now, we substitute back**y = (x+2)**into the factored expression:**(x+2+4)(x+2+1)**.**Simplify:**This simplifies to**(x+6)(x+3)**.

### Final Result

Therefore, the factored form of the expression **(x+2)^2 + 5(x+2) + 4** is **(x+6)(x+3)**.