## Expanding (x+1)(x+2)(x+3)

This article will explore the process of expanding the expression (x+1)(x+2)(x+3). This involves multiplying out the factors to get a polynomial in standard form.

### Expanding the First Two Factors

We start by multiplying the first two factors:

(x+1)(x+2) = x(x+2) + 1(x+2)

Using the distributive property:

= x² + 2x + x + 2

Combining like terms:

= **x² + 3x + 2**

### Expanding the Entire Expression

Now we need to multiply the result by the third factor:

(x² + 3x + 2)(x+3) = x(x² + 3x + 2) + 3(x² + 3x + 2)

Distributing again:

= x³ + 3x² + 2x + 3x² + 9x + 6

Combining like terms:

= **x³ + 6x² + 11x + 6**

### Conclusion

Therefore, the expanded form of (x+1)(x+2)(x+3) is **x³ + 6x² + 11x + 6**. This process demonstrates the use of the distributive property and combining like terms in simplifying polynomial expressions.