- Properties of Real Numbers
- Home
- Identifying Like Terms
- Combining like terms: Whole number coefficients
- Introduction to properties of addition
- Multiplying a constant and a linear monomial
- Distributive property: Whole Number coefficients
- Factoring a linear binomial
- Identifying parts in an algebraic expression
- Identifying equivalent algebraic expressions
- Introduction to properties of multiplication

# Combining like terms: Whole number coefficients

A **term** is a constant or a combination of variables in an expression.

For example, in the equation 15 + 3x^{3} + 2x = 9x - 4,

the terms on the left are 15, 3x^{3} and 2x, while the terms on the right are 9x, and -4.

Terms in algebraic expressions that have the same variable(s) with same exponents are called **like terms**.

**Combining Like Terms** is a method used to simplify an expression or an equation using addition and subtraction of the coefficients of terms.

Consider the expression below

8 + 9

By adding 8 and 9, we can easily find that the expression is equivalent to 17.

Algebraic expressions can be simplified by combining like terms. Consider the algebraic expression below:

18x + 13 + 9x

We see that 18x and 9x are like terms. Therefore, the coefficients, 18 and 9, can be added.

18x + 9x = 27x

So, 18x + 13 + 9x = 27x + 13

**Rules to combine like terms**

We simplify algebraic expressions and equations by combining like terms.

First, we identify sets of like terms.

Now the coefficients of each set of like terms are added.

With the like terms combined, the expression becomes simplified

algebraic equations become easier to be solved

Simplify the following expression by combining like terms:

2x − 10y − 18x + 18y + 21x

### Solution

**Step 1:**

Combining like terms

2x − 10y − 18x + 18y + 21x

= (2x −18x + 21x) + (−10y + 18y)

**Step 2:**

(2x −18x + 21x) + (−10y + 18y) = 5x + 8y

**Step 3:**

So, 2x − 10y − 18x + 18y + 21x

= 5x + 8y

Simplify the following expression by combining like terms:

12a + 8b + 9c + 5a + 7b + 11c

### Solution

**Step 1:**

Combining like terms

12a + 8b + 9c + 5a + 7b + 11c

= (12a + 5a) + (8b + 7b) + (9c + 11c)

**Step 2:**

(12a + 5a) + (8b + 7b) + (9c + 11c)

= 17a + 15b + 20c

**Step 3:**

So, 12a + 8b + 9c + 5a + 7b + 11c

= 17a + 15b + 20c