- Properties of Real Numbers
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- 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

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# Identifying Like Terms

When we look at algebraic terms to find like terms, first we ignore the coefficients and only look if terms have the same variable(s) with same exponents. Those terms which qualify this condition are called **like terms**.

For **example** − Consider the terms, 2a, 5a, 9a, 13a

All the given four terms are like terms, because each of them have the same single variable ‘a’. These terms are having different coefficients but the same variable.

The following are like terms as each term consists of a single variable, x, and a numeric coefficient.

7x, 41x, 3x, 0x, -22x, -x

Each of the following are like terms because they are all constants.

18, -5, 27, 905, 0.8

Each of the following are like terms because they are all y

^{2}with a coefficient.5y

^{2}, 3y^{2}, -y^{2}, 29y^{2}

For comparison, below are a few examples of **unlike terms**.

The following two terms both have a single variable, but the terms are not alike since different variables are used.

13x, 13y

Each y variable in the terms below has a different exponent, therefore these are unlike terms.

11y, 18y

^{2}, 32y^{5}

Identify the like terms in the following expression

5x + 7xy −7x + 11xy

### Solution

**Step 1:**

Like terms consist of same variables raised to same exponents.

There are two pairs of like terms in this expression.

**Step 2:**

They are as follows.

5x and −7x; 7xy and 11xy;

5x and −7x have the same variable x

while 7xy and 11xy have the same combination of variables xy.

Identify the like terms in the following expression:

15m + 2n – 4m + n +12m

### Solution

**Step 1:**

Like terms consist of same variables raised to same exponents.

**Step 2:**

The following are like terms because each term consists of variable, m, and a numeric coefficient.

15m, −4m, 12m

**Step 3:**

The following are like terms because each term consists of variable, n, and a numeric coefficient.

n, 2n