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11-2 Simplifying Algebraic Expressions California Standards Preview of Grade 7 AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, and commutative) and justify the process used. Also covered: 6AF1.2, 6AF3.1, 6AF3.2 Holt CA Course 1 11-2 Simplifying Algebraic Expressions Vocabulary term coefficient Holt CA Course 1 11-2 Simplifying Algebraic Expressions In the expression 7x + 9y, 7x and 9y are called terms. A term can be a number, a variable, or a product of numbers and variables. Terms in an expression are separated by plus or minus signs. In the term 7x, 7 is called the coefficient. A coefficient is a number that is multiplied by a variable in an algebraic expression. Holt CA Course 1 Coefficient Variable 11-2 Simplifying Algebraic Expressions Like terms are terms with the same variable raised to the same power. The coefficients do not have to be the same. Constants, like 5, 1 , 2 and 3.2, are also like terms. Like Terms Unlike Terms Holt CA Course 1 3x and 2x 5x2 and 2x The exponents are different w and w 7 6a and 6b The variables are different 5 and 1.8 3.2 and n Only one term contains a variable 11-2 Simplifying Algebraic Expressions Additional Example 1: Identifying Like Terms Identify like terms in the list. 3t 5w2 7t 9v 4w2 8v Look for like variables with like powers. 3t 5w2 7t 9v Like terms: 3t and 7t 4w2 8v 5w2 and 4w2 9v and 8v Helpful Hint Use different shapes or colors to indicate sets of like terms. Holt CA Course 1 11-2 Simplifying Algebraic Expressions Check It Out! Example 1 Identify like terms in the list. 2x 4y3 8x 5z 5y3 8z Look for like variables with like powers. 2x 4y3 8x 5z Like terms: 2x and 8x Holt CA Course 1 5y3 8z 4y3 and 5y3 5z and 8z 11-2 Simplifying Algebraic Expressions To simplify an algebraic expression that contains like terms, combine like terms. Combining like terms is like grouping similar objects. x x x x 4x + + x x x x 5x x = x x = x x x x x x x 9x To combine like terms that have variables, use the Distributive Property. 4x + 5x = (4 + 5)x = 9x Holt CA Course 1 11-2 Simplifying Algebraic Expressions Additional Example 2: Simplifying Algebraic Expressions Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. A. 6t – 4t 6t – 4t 6t and 4t are like terms. 2t Subtract the coefficients. B. 45x – 37y + 87 In this expression, there are no like terms to combine. Holt CA Course 1 11-2 Simplifying Algebraic Expressions Additional Example 2: Simplifying Algebraic Expressions Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. C. 3a2 + 5b + 11b2 – 4b + 2a2 – 6 3a2 + 5b + 11b2 – 4b + 2a2 – 6 3a2 + 2a2 + 5b – 4b + 11b2 – 6 (3 + 2)a2 + (5 – 4)b + 11b2 – 6 5a2 + b + 11b2 – 6 Holt CA Course 1 Identify like terms. Commutative Property. Distributive Property. 11-2 Simplifying Algebraic Expressions Check It Out! Example 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. A. 5y + 3y 5y + 3y 8y 5y and 3y are like terms. Add the coefficients. B. 2(x2 – 13x) + 6 2x 2 – 26x + 6 Distributive Property. There are no like terms to combine. Holt CA Course 1 11-2 Simplifying Algebraic Expressions Check It Out! Example 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. C. 4x2 + 5y + 3x2 – 4y + 2x2 + 5 4x2 + 5y + 3x2 – 4y + 2x2 + 5 Identify like terms. 4x2 + 3x2 + 2x2 + 5y – 4y + 5 Commutative Property. (4 + 3 + 2)x2 + (5 – 4)y + 5 Distributive Property. 9x2 + y + 5 Holt CA Course 1 11-2 Simplifying Algebraic Expressions Additional Example 3: Geometry Application Write an expression for the perimeter of the triangle. Then simplify the expression. 2x + 3 3x + 2 x 2x + 3 + 3x + 2 + x Write an expression using the side lengths. (2x + 3x + x) + (3 + 2) Identify and group like terms. (2 + 3 + 1)x + (3 + 2) Distributive Property. 6x + 5 Holt CA Course 1 11-2 Simplifying Algebraic Expressions Check It Out! Example 3 Write an expression for the perimeter of the triangle. Then simplify the expression. 2x + 1 2x + 1 x x + 2x + 1 + 2x + 1 x + 2x + 2x + 1 + 1 (1 + 2 + 2)x + (1 + 1) 5x + 2 Holt CA Course 1 Write an expression using the side lengths. Identify and group like terms. Distributive Property.