## Simplifying Polynomial Expressions: A Step-by-Step Guide

In algebra, we often encounter expressions involving variables and their powers. These expressions can be simplified by combining like terms. Let's explore how to simplify the expression:

**(w^3 - 3w^2 + 12w + 8) + (2w^3 - 18w + 4)**

### Step 1: Identify Like Terms

**Like terms**have the same variable and exponent. For example,`w^3`

and`2w^3`

are like terms, while`w^3`

and`w^2`

are not.

Let's identify the like terms in our expression:

**w^3 terms:**`w^3`

and`2w^3`

**w^2 terms:**`-3w^2`

(there's no other w^2 term)**w terms:**`12w`

and`-18w`

**Constant terms:**`8`

and`4`

### Step 2: Combine Like Terms

Now we combine the coefficients of like terms:

**w^3 terms:**`w^3 + 2w^3 = 3w^3`

**w^2 terms:**`-3w^2`

(remains the same)**w terms:**`12w - 18w = -6w`

**Constant terms:**`8 + 4 = 12`

### Step 3: Write the Simplified Expression

Finally, we combine all the simplified terms:

**(w^3 - 3w^2 + 12w + 8) + (2w^3 - 18w + 4) = ** **3w^3 - 3w^2 - 6w + 12**

Therefore, the simplified form of the given expression is **3w^3 - 3w^2 - 6w + 12**.