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2-2 Simplifying Expressions

Video Tutor Help Evaluating algebraic expressions with more than one variableEvaluating algebraic expressions with more than one variable (2-2) Using properties of additionUsing properties of addition (2-2) Finding the greatest common factor using prime factorizationFinding the greatest common factor using prime factorization (2-2) Properties Expanding Expressions Khan Academy Brain Pop The distributive property

Video Tutor Help Vocabulary (Electronic) Flash Cards Exponents, Factors, and Fractions Vocabulary 2A: Graphic Organizer Vocabulary 2B: Reading Comprehension Vocabulary 2C: Reading/Writing Math Symbols Vocabulary 2D: Visual Vocabulary Practice Vocabulary 2E: Vocabulary C Vocabulary 2F: Vocabulary Review Puzzle

Worksheets Daily Notetaking Guide Worksheets Version A Practice, Guided Problem Solving Lesson 2-2 Practice 2-2 Guided Problem Solving 2-2

Vocabulary Practice Vocabulary 1A: Graphic Organizer Vocabulary 1B: Reading Comprehension Vocabulary 1C: Reading/Writing Math Symbols Vocabulary 1D: Visual Vocabulary Practice Vocabulary 1E: Vocabulary C Vocabulary 1F: Vocabulary Review Puzzle Vocabulary (Electronic) Flash Cards

Additional Lesson Examples Step-by-Step Examples Lesson 2-2

Lesson Readiness Lesson Quiz Problem of the Day Lesson 2-2

Terms When a plus sign separates an algebraic expression into parts, each part is called a term. The numerical factor of a term that contains a variable is called the coefficient of the variable. -2x x This expression has three terms. -2 is the coefficient of -2x 1 is the coefficient of x.

Like Terms Like terms contain the same variables, such as 2x and x. A term without a variable is called a constant. Constant terms are also like terms. 4a a + 9 Constants and like terms Like terms

Teaching Tip If an expression has no plus or minus signs, the entire expression is a term.

Equivalent Expressions 2(4 + 3) = 2(4) + 2(3) = Distributive Property = 14 Multiply. Then add. 2(x + 3) = 2(x) + 2(3) Distributive Property = 2x + 6 Multiply The expressions 2(x + 3) and 2x + 6 are equivalent expressions, because no matter what x is, these expressions have the same value.

Simplest Terms An algebraic expression is in simplest form if it has no like terms and no parentheses. You can use Distributive Property to combine like terms. This is called simplifying the expression.

Example 2-1a Definition of subtraction Identity Property Answer: The terms are 4x, –x, 2y, and –3. The like terms are 4x and –x. The coefficients are 4, –1, and 2. The constant is –3. Identify the terms, like terms, coefficients, and constants in the expression Identify Parts of Expressions

Example 2-1b Answer: The terms are 5x, 3y, –2y, and 6. The like terms are 3y and –2y. The coefficients are 5, 3, and –2. The constant is 6. Identify the terms, like terms, coefficients, and constants in the expression

Example 2-2a Simplify. 5x and 4x are like terms. Simplify. Answer: 9x Distributive Property Simplify Algebraic Expressions

Example 2-2b Simplify. 8n and 4n are like terms. Distributive Property Simplify. Answer: Commutative Property Simplify Algebraic Expressions

Example 2-2c Simplify. 6x and –5x are like terms. 4 and –7 are also like terms. Commutative Property Distributive Property Definition of subtraction Simplify Algebraic Expressions

Example 2-2d Answer: Simplify.

Example 2-2e Simplify. Multiply. Identity Property Distributive Property Commutative Property Simplify Algebraic Expressions

Example 2-2f Answer: Distributive Property Simplify.

Example 1-1a Simplify. Answer: Use the Distributive Property to rewrite. Write Equivalent Expressions

Example 1-1b Answer: Use the Distributive Property to rewrite

Example 1-2a Answer: Use the Distributive Property to rewrite Simplify. Write Equivalent Expressions

Example 1-2b Answer: Use the Distributive Property to rewrite

Example 1-3a Answer: Distributive Property Simplify. Definition of subtraction Use the Distributive Property to rewrite Rewrite Write Expressions with Subtraction

Example 1-3b Answer: Use the Distributive Property to rewrite

Example 1-4a Answer: Distributive Property Simplify. Rewrite Use the Distributive Property to rewrite Write Expressions with Subtraction

Example 1-4b Answer: Use the Distributive Property to rewrite