Evaluate Algebraic Expressions

In the last section, we streamlined expressions utilizing the stimulate of operations. In this section, we’ll advice expressions—again following the stimulate of operations.

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To evaluate an algebraic expression method to discover the worth of the expression when the change is replaced by a given number. To advice an expression, us substitute the provided number for the variable in the expression and also then simplify the expression using the stimulate of operations.

Identify Terms, Coefficients, and also Like Terms

Algebraic expression are comprised of terms. A term is a continuous or the product that a continuous and one or more variables. Some examples of terms room (7), (y), (5x^2), (9a), and (13xy).

The constant that multiplies the variable(s) in a ax is referred to as the coefficient. We can think the the coefficient together the number in front of the variable. The coefficient that the term (3x) is (3). As soon as we create (x), the coefficient is (1), due to the fact that (x = 1 • x). Table (PageIndex1) offers the coefficients because that each the the terms in the left column.

Table (PageIndex1) ax Coefficient
7 7
9a 9
y 1
5x2 5

An algebraic expression might consist the one or much more terms added or subtracted. In this chapter, we will certainly only work-related with terms that are included together. Table (PageIndex2) offers some instances of algebraic expression with miscellaneous numbers that terms. Notice that we include the operation prior to a term v it.

Table (PageIndex2) Expression terms
7 7
y y
x + 7 x, 7
2x + 7y + 4 2x, 7y, 4
3x2 + 4x2 + 5y + 3 3x2, 4x2, 5y, 3

exercise (PageIndex14)

Identify every terms in the given expression, and their coefficients: (9a + 13a^2 + a^3)


The terms room (9a, 13a^2,) and also (a^3), The coefficients are (9, 13,) and also (1).

Some terms share usual traits. Look at the following terms. Which ones it seems to be ~ to have traits in common?

(5x, 7, n^2, 4, 3x, 9n^2)

Which of this terms are like terms?

The terms (7) and also (4) room both consistent terms. The terms (5x) and (3x) space both terms with (x). The terms (n^2) and (9n^2) both have (n^2).

Terms are called like state if they have the very same variables and also exponents. All consistent terms are additionally like terms. So among the state (5x, 7, n^2, 4, 3x, 9n^2, 7) and also (4) are prefer terms, (5x) and also (3x) are favor terms, and also (n^2) and (9n^2) are like terms.

Simplify expression by Combining choose Terms

We deserve to simplify an expression by combining the like terms. What execute you think (3x + 6x) would certainly simplify to? If you thought (9x), you would certainly be right!

We can see why this functions by writing both terms as addition problems.


Add the coefficients and also keep the same variable. It doesn’t matter what (x) is. If you have actually (3) of something and include (6) more of the exact same thing, the result is (9) the them. For example, (3) oranges plus (6) oranges is (9) oranges. We will discuss the sirhenryjones-museums.orgematical properties behind this later.

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The expression (3x + 6x) has only two terms. Once an expression contains more terms, it may be advantageous to rearrange the state so that favor terms are together. The Commutative property of enhancement says that we can readjust the order of addends without an altering the sum. So we could rearrange the following expression prior to combining prefer terms.