OBJECTIVES 2.6 Introduction to Algebra and Expressions Slide 1Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aEvaluate an algebraic expression by substitution. bUse the distributive law to find equivalent expressions.

2.6 Introduction to Algebra and Expressions a Evaluate an algebraic expression by substitution. Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When a letter can stand for various numbers, we call the letter a variable. A number or a letter that stands for just one number is called a constant. Let c = the speed of light. Then c is a constant. Let a = the speed of a car. Then a is a variable since the value of a can vary.

2.6 Introduction to Algebra and Expressions a Evaluate an algebraic expression by substitution. Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. An algebraic expression consists of variables, constants, numerals, and operation signs. When we replace a variable with a number, we say that we are substituting for the variable. Carrying out the operations of addition, subtraction, and so on, is called evaluating the expression.

EXAMPLE 2.6 Introduction to Algebra and Expressions a Evaluate an algebraic expression by substitution. 1 Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

2.6 Introduction to Algebra and Expressions a Evaluate an algebraic expression by substitution. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 2.6 Introduction to Algebra and Expressions a Evaluate an algebraic expression by substitution. 2 Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

2.6 Introduction to Algebra and Expressions a Evaluate an algebraic expression by substitution. Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 2.6 Introduction to Algebra and Expressions a Evaluate an algebraic expression by substitution. 3 Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Title 2.6 Introduction to Algebra and Expressions Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 2.6 Introduction to Algebra and Expressions a Evaluate an algebraic expression by substitution. 6 Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 2.6 Introduction to Algebra and Expressions b Use the distributive law to find equivalent expressions. 8 Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

2.6 Introduction to Algebra and Expressions EQUIVALENT EXPRESSIONS Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Two expressions that have the same value for all allowable replacements are called equivalent.

2.6 Introduction to Algebra and Expressions b Use the distributive law to find equivalent expressions. Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. An important concept, known as the distributive law, is useful for finding equivalent algebraic expressions. The distributive law involves two operations: multiplication and either addition or subtraction.

2.6 Introduction to Algebra and Expressions b Use the distributive law to find equivalent expressions. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To carry out the multiplication, we actually added two products. That is, The distributive law says that if we want to multiply a sum of several numbers by a number, we can either add within the grouping symbols and then multiply, or multiply each of the terms separately and then add.

2.6 Introduction to Algebra and Expressions THE DISTRIBUTIVE LAW Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 2.6 Introduction to Algebra and Expressions b Use the distributive law to find equivalent expressions. 9 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The parentheses in the statement of the distributive law tell us to multiply both b and c by a. Without the parentheses, we would have ab + c.

EXAMPLE 2.6 Introduction to Algebra and Expressions b Use the distributive law to find equivalent expressions. 11 Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Use the distributive law to write an expression equivalent to each of the following:

EXAMPLE 2.6 Introduction to Algebra and Expressions b Use the distributive law to find equivalent expressions. 11 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 2.6 Introduction to Algebra and Expressions b Use the distributive law to find equivalent expressions. 11 Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 2.6 Introduction to Algebra and Expressions b Use the distributive law to find equivalent expressions. 11 Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 2.6 Introduction to Algebra and Expressions b Use the distributive law to find equivalent expressions. 11 Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.