We can roughly describe **like terms** as algebraic expressions that have common variables and the same exponents. The coefficients don't need to be identical. If they are like terms, we can combine them by addition or subtraction.

The best way to learn about like terms is through examples.

These are some examples of like/similar terms.

\( \Rightarrow \) \(3\) and \(-5\) are like terms because they are both constants.

\( \Rightarrow \) \(7x\) and \(2x\) are like terms because they have the same variable \(x\).

\( \Rightarrow \) \( - 4{y^2}\) and \(9{y^2}\) are like terms because not only they have the same variable \(y\) but the values of their exponents are also the same which is \(2\).

\( \Rightarrow \) \(6a{b^2}\) and \( - 2a{b^2}\) are like terms because they have common group of variables and the exponent of each variable matches.

**Example 1:** Combine the like terms below.

$$a + 2b + 3c$$

The variables \(a\), \(b\), and \(c\) are different variables therefore they are NOT like terms. That means we can't combine them.

**Example 2:** Combine the like terms below.

$$3x - 5y + x + 4y$$

Notice that \(3x\) and \(x\) are like terms. In the same way, \(-5y\) and \(4y\) are like terms. Since they are like terms, we can combine them by adding or subtracting. We can put them side by side for clarity. Thus, we have

$$3x + x - 5y + 4y$$

$$4x - y$$

**Example 3:** Combine the like terms below.

$$6mn - m{n^2} - {m^2}n - 5mn + 3m{n^2} - {m^2}n$$

What we can do is to put the like terms side by side. Then, we operate them by adding or subtracting.

$$6mn - 5mn = mn$$

$$ - m{n^2} + 3m{n^2} = 2m{n^2}$$

$$ - {m^2}n - {m^2}n = - 2{m^2}n$$

We can put them together to write our final answer.

$$mn + 2m{n^2} - 2{m^2}n$$

**Example 4:** Simplify by combining like terms.

$$10 - {r^2} - 4j{r^2} - 7 + 3{r^2} + 4j{r^2} + jr$$

Just like in our previous example, let's put the like terms side by side.

The numbers are like terms.

$$10 - 7 = 3$$

The \(r^2\)'s are like terms.

$$ - {r^2} + 3{r^2} = 2{r^2}$$

The \(jr^2\)'s are like terms.

$$ - 4j{r^2} + 4j{r^2} = 0$$

The \(jr\) is by itself. Nothing to combine with.

$$jr$$

Putting them back together, we have

$$2{r^2} + jr + 3$$