Core Focus on Introductory Algebra

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Presentation transcript:

Core Focus on Introductory Algebra Lesson 2.7 Core Focus on Introductory Algebra Using The Distributive Property With Variables

Warm-Up Find the product of each expression using the Distributive Property. 1. 3(799) 2. 6(12.2) 3. 805(4) 2,397 73.2 3,220

Using the Distributive Property with Variables Lesson 2.7 Using the Distributive Property with Variables Simplify expressions with variables.

Vocabulary Equivalent Expressions Two algebraic expressions which represent the same simplified algebraic expression.

Good to Know! 3(x + 4) = 3(x) + 3(4) = 3x + 12 Many algebraic expressions have parentheses. In order to simplify algebraic expressions with parentheses, the Distributive Property must be used. Multiply the front factor by each term in the parentheses. 3(x + 4) = 3(x) + 3(4) = 3x + 12 Algebraic expressions or equations often have like terms that can be combined. If there are parentheses involved in the expression, the Distributive Property must be used FIRST before combining like terms. 2y + 4(y + 5) − 1 = 2y + 4y + 20 − 1 = 6y + 19

Example 1 Use the Distributive Property to simplify each expression. a. 2(x + 6) b. 5(y − 8) c. 4(3x − 2) = 2(x) + 2(6) = 2x + 12 = 5(y) − 5(8) = 5y − 40 = 4(3x) − 4(2) = 12x − 8 ` Only multiply the two coefficients together. Think of it as 4 groups of 3x.

Example 2 Simplify by distributing and combining like terms. 5(x + 4) + 3x + 3 Distribute first. 5(x + 4) + 3x + 3 = 5x + 20 + 3x + 3 Use the Commutative Property 5x + 3x + 20 + 3 to group like terms. Combine like terms. 8x + 23 5(x + 4) + 3x + 3 = 8x + 23

Explore! Equivalent Expressions Two algebraic expressions are equivalent expressions if they represent the same simplified algebraic expression. In this matching game, each card in the deck has an algebraic expression on it. The goal of the game is to match the six LETTER Expression Cards (A, B, C...) to their equivalent NUMBER Expression Cards (1, 2, 3...). For the cards on the next slide: Step 1 Simplify each LETTER Expression Card. Step 2 Match each LETTER Expression Card to its equivalent NUMBER Expression Card. Step 3 Create two more LETTER Expression Cards and corresponding NUMBER Expression Cards to be used in a future matching game.

Explore! Equivalent Expressions

Communication Prompt What is the process for simplifying an expression that contains parentheses and like terms?

Exit Problems Simplify each expression. 1. 7(x + 3) 2. 2(5y − 8) 3. 3(x + 4) + 2x − 1 4. 6 + 2(7x − 1) 7x + 21 10y − 16 5x + 11 4 + 14x