### Introduction

Combining like terms is a fundamental process in algebra that simplifies expressions. **Like terms** are terms that have the same variables raised to the same power, even if they have different coefficients.

### Identifying Like Terms

To combine like terms, you first **identify the terms** that have the same variables and exponents. For example, in the expression:

$3x^2 + 5x - 2x + 4 - x^2$
The like terms are:

- $3x^2$ and $-x^2$ (both have the variable $x$ raised to the power of 2)
- $5x$ and $-2x$ (both have the variable $x$ raised to the power of 1)

### Combining the Terms

**Group the like terms** together.
**Add or subtract their coefficients**.

For the expression given above, we can group and then combine like terms:

$3x^2 - x^2 + 5x - 2x + 4$
Combining the coefficients of the like terms, we get:

$3x^2 - x^2 = 2x^2$
$5x - 2x = 3x$
So, the simplified expression is:

$2x^2 + 3x + 4$
### Special Cases

**Constants**, or terms without variables, are also considered like terms with each other. For instance, in the expression:

$7 + 3x + 5 - 2x$
The constants $7$ and $5$ can be combined:

$7 + 5 = 12$
Resulting in the simplified form:

$3x - 2x + 12$
$x + 12$
### Benefits

Combining like terms:

**Simplifies expressions**, making them easier to work with.
**Reduces complexity**, especially useful in solving equations or inequalities.

### Example

Let's look at another example:

$4y + 7 - 5y + 3 + 2y$
First, **group the like terms**:

$(4y - 5y + 2y) + (7 + 3)$
Now, **combine the coefficients**:

$(4y - 5y + 2y) = (4 - 5 + 2)y = 1y = y$
$7 + 3 = 10$
The simplified expression is:

$y + 10$
Being proficient at combining like terms is essential for simplifying algebraic expressions and solving algebra problems effectively.