PRE-ALGEBRA

Lesson 2-3 Warm-Up

PRE-ALGEBRA What is a “term”? What is a “constant”? What is a “coefficient”? What are “like terms”? term: a number, a variable, or the product of a number and one or more variables. Examples: 4, x, 4x, 4xyz constant: a term that has no variable Examples: 5, 104 coefficient: the numerical (number) part of a term that has variable Examples: Like terms: terms that have exactly the same variable or variable factors (variables multiplied together) Simplifying Algebraic Expressions (2-3)

PRE-ALGEBRA How can you combine like terms? You can combine like terms by adding or subtracting their coefficients (numbers in front of the shares variable or variables) using the Distributive Property. Note: Often a variable does not have a coefficient (number in front of it). In this case, there is an understood “1” in front of the variable which is removed by the Identity Property of Multiplication. Examples: b is the same as 1b and -a is the same as -1a Simplifying Algebraic Expressions (2-3)

PRE-ALGEBRA Name the coefficients, the like terms, and the constants in 7x + y – 2x – 7. Coefficients: 7, 1, –2Like terms: 7x, –2xConstant: –7 Simplifying Algebraic Expressions LESSON 2-3 Additional Examples

PRE-ALGEBRA How can you use a model to simplify an algebraic expression? To simplify an algebraic expression using a model, model each part of the expression (example: 1x = a green bar; 1 = a yellow square) and then combine like terms (green bars with each other and yellow squares with each other). Example: Simplify 2x x. Model each part of the expression. Combine like terms. Simplifying Algebraic Expressions (2-3) 1 x x 1 1 1

PRE-ALGEBRA Simplify 9 + 4f f f f 6f + 12 Simplifying Algebraic Expressions LESSON 2-3 Additional Examples

PRE-ALGEBRA How does the Distributive Property allow you to combine like terms? The Distributive Property allows you to combine like terms by adding or subtracting the coefficients of like terms, because the variable(s) is / are shared. Example: Simplify 5y + y. Example: Evaluate 4g g for g = 5. Simplifying Algebraic Expressions (2-3)

PRE-ALGEBRA Simplify 2b + b – 4. 2b + b – 4 = 2b + 1b – 4 Use the Identity Property of Multiplication. = (2 + 1)b – 4 Use the Distributive Property to combine like terms. = 3b – 4 Simplify. Simplifying Algebraic Expressions LESSON 2-3 Additional Examples

PRE-ALGEBRA Evaluate (7 – 3x)5 + 20x for x = 2. (7 – 3x)5 + 20x = 35 – 15x + 20x Distributive Property = 35 + (– )xCombine like terms. = x Simplify. = (2)Substitute. = 45Simplify. Simplifying Algebraic Expressions LESSON 2-3 Additional Examples

PRE-ALGEBRA Name coefficients, like terms, and constants. 1.4f – 2f z + 2y – 14 Simplify each expression. 3.3(a + c – 1) – 2c 4.4(4v) – 4(v – 9) 3a + c – 3 4, –2; 4f, –2f; 31, 2; none; –14 12v + 36 Simplifying Algebraic Expressions LESSON 2-3 Lesson Quiz