Evaluate Algebraic Expressions

In the critical section, we streamlined expressions making use of the bespeak of operations. In this section, we’ll advice expressions—again following the order of operations.

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To evaluate an algebraic expression method to uncover the worth of the expression as soon as the variable is changed by a given number. To evaluate an expression, us substitute the given number for the variable in the expression and then leveling the expression using the order of operations.

Identify Terms, Coefficients, and also Like Terms

Algebraic expressions are comprised of terms. A term is a continuous or the product that a constant 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 term is called the coefficient. We have the right to think the the coefficient as the number in front of the variable. The coefficient of the ax \\(3x\\) is \\(3\\). Once we write \\(x\\), the coefficient is \\(1\\), due to the fact that \\(x = 1 • x\\). Table \\(\\PageIndex1\\) provides the coefficients because that each of the state in the left column.

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

An algebraic expression might consist that one or an ext terms added or subtracted. In this chapter, we will only work-related with terms the are included together. Table \\(\\PageIndex2\\) offers some instances of algebraic expression with assorted numbers of terms. An alert that we include the operation prior to a term with it.

Table \\(\\PageIndex2\\) Expression state
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 all terms in the provided expression, and also their coefficients: \\(9a + 13a^2 + a^3\\)


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

Some terms share usual traits. Look at the adhering to terms. Which ones seem to have actually traits in common?

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

Which of this terms are favor terms?

The terms \\(7\\) and also \\(4\\) room both constant terms. The state \\(5x\\) and also \\(3x\\) room both terms through \\(x\\). The terms \\(n^2\\) and \\(9n^2\\) both have actually \\(n^2\\).

Terms are referred to as like state if they have actually the same variables and exponents. All constant terms are likewise like terms. So amongst the terms \\(5x, 7, n^2, 4, 3x, 9n^2, 7\\) and \\(4\\) are like terms, \\(5x\\) and \\(3x\\) are like terms, and \\(n^2\\) and \\(9n^2\\) are like terms.

Simplify expression by Combining prefer Terms

We can simplify one expression by combining the favor terms. What execute you think \\(3x + 6x\\) would certainly simplify to? If you assumed \\(9x\\), you would be right!

We deserve to see why this works by creating both state as addition problems.


Add the coefficients and also keep the very same variable. It doesn’t matter what \\(x\\) is. If you have actually \\(3\\) of other and include \\(6\\) much more of the same thing, the result is \\(9\\) that them. For example, \\(3\\) oranges to add \\(6\\) oranges is \\(9\\) oranges. Us will comment on the medtox.orgematical properties behind this later.

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The expression \\(3x + 6x\\) has only 2 terms. Once an expression contains much more terms, it might be advantageous to rearrange the terms so that favor terms are together. The Commutative residential or commercial property of enhancement says that us can adjust the order of addends without an altering the sum. For this reason we can rearrange the complying with expression prior to combining prefer terms.