# Mathematical definition of like terms

Like Terms. "Like terms" are terms whose variables (and their exponents such as the 2 in x2) are the same. In other words, terms that are "like" each other.

Thus algebra enables us to write down general statements clearly and concisely. The development of mathematics was significantly restricted before the 17th century by the lack of efficient algebraic language and symbolism. How this notation evolved will be discussed in the History section. Because the letters are simply stand-ins for numbers, arithmetic is carried out exactly as it is with numbers.

In particular the laws of arithmetic commutative, associative and distributive hold.

In this module we will use the word pronumeral for the letters used in algebra. The terms such as variable and parameter cannot be precisely defined at this stage and are best left to be introduced later in the development of algebra. An algebraic expression is an expression involving numbers, parentheses, operation signs and pronumerals that becomes a number when numbers are substituted for the pronumerals.

As discussed later in this module the multiplication sign is omitted between letters and between a number and a letter. In this module, the emphasis is on expressions, and on the connection to the arithmetic that students have already met with whole numbers and fractions. The values of the pronumerals will therefore be restricted to the whole numbers and non-negative fractions.

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• 1. Addition and Subtraction of Algebraic Expressions.
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In algebra, pronumerals are used to stand for numbers. You may or may not know what the value of x is although in this example we do know that x is a whole number. The following table gives us some meanings of some commonly occurring algebraic expressions.

In algebra there are conventional ways of writing multiplication, division and indices. We have been following this convention earlier in this module. It is conventional to write the number first. Instead the alternative fraction notation for division is used. Assigning values to a pronumeral is called substitution. Adding and subtracting like terms. If you have 3 pencil case with the same number x of pencils in each, you have 3 x pencils altogether.

This can be done as the number of pencils in each case is the same. The terms 3 x and 2 x are said to be like terms. Consider another example. The terms 2 xy and xy are like terms. Two terms are called like terms if they involve exactly the same pronumerals and each pronumeral has the same index.

The distributive law explains the addition and subtraction of like terms. For example:. The terms 2 x and 3y are not like terms because the pronumerals are different. The terms 3 x and 3x 2 are not like terms because the indices are different.

## Combining Like Terms

There are no like terms for 2 y , so by using the commutative law for addition the sum is. The any-order principle for addition is used for the adding like terms. Because of the commutative law and the associative law for multiplication any-order principle for multiplication the order of the factors in each term does not matter.

Brackets fulfill the same role in algebra as they do in arithmetic. Brackets are used in algebra in the following way. Let x be the number.

### Identify Terms, Coefficients, and Like Terms

For a party, the host prepared 6 tins of chocolate balls, each containing n chocolate balls. Each crate of bananas contains n bananas. Three bananas are removed from each crate. Algebraic expressions are combinations of variables , numbers, and at least one arithmetic operation. Term: Each expression is made up of terms.

A term can be a signed number, a variable, or a constant multiplied by a variable or variables. Factor: Something which is multiplied by something else. A factor can be a number, variable, term, or a longer expression. Coefficient: The numerical factor of a multiplication expression that contains a variable. In the first term, 2 x , the coefficient is 2 : in the second term, 4 y , the coefficient is 4.

Constant: A number that cannot change its value. Like Terms: Terms that contain the same variables such as 2 m , 6 m or 3 x y and 7 x y. If an expression has more than one constant terms, those are also like terms. Difference of a number and 7. Step 1: Multiply the radical expression.

## Monomials and polynomials

Using the distributive property found in Tutorial 5: Properties of Real Numbers we get:. These are practice problems to help bring you to the next level.

It will allow you to check and see if you have an understanding of these types of problems. Math works just like anything else, if you want to get good at it, then you need to practice it. Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument. In fact there is no such thing as too much practice.

## Combining Like Terms

The following are two examples of two different pairs of like radicals:. Let's see what we get when we simplify the first radical:. Let's see what we get when we simplify the second radical:. Let's see what we get when we simplify the third radical:.

1. Basic Algebra.
2. Combining Like Terms?
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