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Welcome to our Math lesson on Terms of Algebraic Expressions, this is the third lesson of our suite of math lessons covering the topic of The Meaning of Expressions. Simplifying Expressions, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Any number, letter, group of letters or number-letter combination separated by the symbols 'plus' or 'minus' from the rest of expression is called the 'term' of the algebraic expression. The sign is counted with the term that comes after it.
For example, the algebraic expression
contains four different terms, namely 3, -4x, 2y3 and -z/3.
If two or more terms of an algebraic expression have the same combination of letters, they are called 'like terms'. Like terms are important in an algebraic expression as we can add or subtract like terms with each other. For example, in the above algebraic expression we cannot do any operation with its terms, as there are no like terms in it.
All terms of algebraic expressions begin with a number called 'coefficient'. A number that is not followed by a letter is known as a 'constant'. Thus, in the algebraic expression above, the numbers 4, 2 and -1/3 are coefficients while 3 is a constant.
If there is no number written before a variable, the coefficient is taken as 1 (or -1 when the term is preceded by a negative sign). This derives from the identity element of multiplication (1 · a = a · 1 = a).
On the other hand, if there is no constant in an algebraic expression, it is taken as 0. This derives from the identity element of addition (0 + a = a + 0 = a).
For example, the coefficients of the algebraic expression
are 5 and -1, while the constant is 0.
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