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7 x + 5 – 3 y 2 + y +

In the expression 7 x + 9 y + 15, 7 x , 9 y , and 15 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 + and –. x 3. 7 x + 5 – 3 y 2 + y +. term. term. term. term. term.

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7 x + 5 – 3 y 2 + y +

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  1. In the expression 7x + 9y + 15, 7x, 9y, and 15 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 + and –. x 3 7x + 5 – 3y2 + y + term term term term term In the term 7x, 7 is called the coefficient. A coefficient is a number that is multiplied by a variable in an algebraic expression. A variable by itself, like y, has a coefficient of 1. So y = 1y. Coefficient Variable 7 x

  2. Like terms are terms with the same variables raised to the same exponents. The coefficients do not have to be the same. Constants, like 5, , and 3.2, are also like terms. 1 2 w 7 3x and 2x w and 5 and 1.8 5x2 and 2x 6a and 6b 3.2 and n Only one term contains a variable The exponents are different. The variables are different

  3. Helpful Hint Use different shapes or colors to indicate sets of like terms. 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 4w2 8v Like terms: 3t and 7t 5w2 and 4w2 9v and 8v

  4. 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 5y3 8z Like terms: 2x and 8x 4y3 and 5y3 5z and 8z

  5. Combining like terms is like grouping similar objects. x x x x x x x x + = x x x x x x x x x x = 9x 4x + 5x To combine like terms that have variables, add or subtract the coefficients.

  6. Additional Example 2: Simplifying Algebraic Expressions Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. A. 6t – 4t 6t and 4t are like terms. 6t– 4t 2t Subtract the coefficients. B. 45x – 37y + 87 In this expression, there are no like terms to combine.

  7. 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 Identify like terms. 3a2 + 5b+ 11b2 – 4b + 2a2 – 6 Group like terms. (3a2 + 2a2) + (5b – 4b)+ 11b2 – 6 5a2 + b + 11b2 – 6 Add or subtract the coefficients.

  8. 2 2x – 26x + 6 Check It Out: Example 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. A. 5y + 3y 5y and 3y are like terms. 5y+ 3y 8y Add the coefficients. B. 2(x2 – 13x) + 6 Distributive Property. There are no like terms to combine.

  9. Check It Out: Example 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. C. 4x2 + 4y + 3x2 – 4y + 2x2 + 5 4x2 + 4y + 3x2 – 4y + 2x2 + 5 Identify like terms. (4x2 + 3x2 +2x2)+ (4y – 4y) + 5 Group like terms. Add or subtract the coefficients. 9x2 + 5

  10. Additional Example 3: Geometry Application Write an expression for the perimeter of the triangle. Then simplify the expression. 2x + 3 3x + 2 x Write an expression using the side lengths. 2x + 3 + 3x + 2 + x Identify and group like terms. (x+ 3x + 2x) + (2 + 3) 6x + 5 Add the coefficients.

  11. Check It Out: Example 3 Write an expression for the perimeter of the triangle. Then simplify the expression. 2x + 1 2x + 1 x Write an expression using the side lengths. x + 2x + 1 + 2x + 1 (x + 2x + 2x) + (1 + 1) Identify and group like terms. 5x + 2 Add the coefficients.

  12. Lesson Quiz: Part I Identify like terms in the list. 1. 3n2 5n 2n3 8n 2.a5 2a2a3 3a 4a2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. 3. 4a + 3b + 2a 4.x2 + 2y + 8x2 5n, 8n 2a2, 4a2 6a + 3b 9x2 + 2y

  13. Lesson Quiz: Part II 5. Write an expression for the perimeter of the given figure. 2x + 3y x + y x + y 2x + 3y 6x + 8y

  14. Lesson Quiz for Student Response Systems 1. Identify the like terms in the list. 6a, 5a2, 2a, 6a3, 7a A. 6a and 2a B. 6a, 5a2, and 6a3 C. 6a, 2a, and 7a D. 5a2 and 6a3

  15. Lesson Quiz for Student Response Systems 2. Identify the like terms in the list. 16y6, 2y5, 4y2, 10y, 16y2 A. 16y6 and 16y2 B. 4y2 and 16y2 C. 16y6 and 2y2 D. 2y5 and 10y

  16. Lesson Quiz for Student Response Systems 3. Simplify 5x + 2y + 7x. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. A. 5x + 2y + 7x = 5x + 7x + 2y Associative Property = (5x + 7x) + 2y Commutative Property = 12x + 2y Add the coefficients. B. 5x + 2y + 7x = 5x + 7x + 2y Commutative Property = (5x + 7x) + 2y Associative Property = 12x + 2y Add the coefficients.

  17. Lesson Quiz for Student Response Systems 4. Simplify 5x2 + 3x + 8x2. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. A. 5x2 + 3x + 8x2 = 5x2 + 8x2 + 3x Commutative Property = (5x2 + 8x2) + 3xAssociative Property = 13x2 + 3x Add the coefficients. B. 5x2 + 3x + 8x2 = 3x + 5x2 + 8x2 Associative Property = (3x + 5x2) + 8x2Commutative Property = 8x + 8x2 Add the coefficients.

  18. Lesson Quiz for Student Response Systems 5. Identify an expression for the perimeter of the given figure. A. (4x + 5y)(x + 2y)C. 10x + 14y B.D. 5x + 7y 4x + 5y x + 2y

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