Prentice Hall's Online Lesson Quiz Enter Web Code: aga–0102
Simplify the expressions inside grouping symbols, such as parentheses, brackets, braces, and fraction bars.
Evaluate all powers.
Do all multiplications and divisions from left to right.
Do all additions and subtractions from left to right.
Example 1:
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An algebraic expression contains at least one variable. You can evaluate an expression by replacing each variable with a value and then applying the rules for the order of operations.
Example 2:
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Evaluate
the expression below, given: a = –5, b = 0.25, c = 3, and d = 8 |
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In an algebraic expression such as –3x + 7, the parts that are added are called terms. A term is a number, a variable or the product of a number and one or more variables. The numerical factor in a term is the coefficient. For example, in the expression 5x – 2y you can think of this expressions as the sum of 5x + (– 2y)to determine that the coefficient of y is –2.
It is important to note that multiplication is the "glue" that holds each term together and addition (or subtraction) separates terms in an expression.
You can simplify expressions by combining like terms. Like terms have the same variables raised to the same powers.
| Like terms: | 3x2 and –5x2 | xy3 and –8xy3 |
When simplifying expressions, it is often said that you are combining like terms. The simplified expressions are equivalent to the original expressions after you combine like terms. Some key concepts and problem areas for students are listed below.
| Properties for Simplifying Algebraic Expressions | |
| Let a, b, and c represent real numbers. | |
| Definition of Subtraction | a – b = a + (– b) |
| Definition of Division |
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| Distributive Property for Subtraction | a( b – c) = ab – ac |
| Multiplication by 0 | 0 · a = 0 |
| Multiplication by –1 | –1· a = – a |
| Opposite of a Sum | –(a + b) = – a + (– b) |
| Opposite of a Difference | –(a – b) = – a – (– b) = b – a |
| Opposite of a Product | –(ab) = –a · b = a · (– b) |
| Opposite of an Opposite | – (– a ) = a |
One dangerous area when evaluating expressions occurs when the leading coefficient in an expression is negative one. Some examples to watch for are shown below. The key element to understand is that the negative one coefficient is separate from the variable and must be evaluated accordingly.
| –x2 for x = 3 | –1·(3)2 = – 9 |
| –x3 for x = 3 | –1· (3)3 = – 27 |
| (–x2 )for x = 3 | (– 1 · 3)2 = ( – 3)2 = 9 |
| (–x3) for x = 3 | (– 1 · 3)3 = ( – 3)3 = – 27 |
| –x2 for x = – 3 | – 1· ( – 3)2 = –1 ·(9) = – 9 |
| –x3 for x = – 3 | –1· ( – 3)3 = –1(– 27) = – 27 |
| (–x)2 for x = – 3 | [(–1)( – 3)]2 = [ 3]2 = 9 |
| (–x)3 for x = – 3 | [(–1)( – 3)]3 = [3]3 = 27 |