Simplifying Algebraic Expressions Warm Up Problem of the

Simplifying Algebraic Expressions Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Simplifying Algebraic Expressions Warm Up Evaluate each expression for y = 3. 1. 3 y + y 2. 7 y 12 21 3. 10 y – 4 y 18 4. 9 y 27 5. y + 5 y + 6 y 36

Simplifying Algebraic Expressions Problem of the Day Emilia saved nickels, dimes, and quarters in a jar. She had as many quarters as dimes, but twice as many nickels as dimes. If the jar had 844 coins, how much money had she saved? $94. 95

Simplifying Algebraic Expressions Learn to simplify algebraic expressions.

Simplifying Algebraic Expressions Vocabulary term coefficient

Simplifying Algebraic Expressions 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 –. 7 x + 5 – 3 y 2 + y + x 3 term term In the term 7 x, 7 is called the Coefficient 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 = 1 y. Variable

Simplifying Algebraic Expressions 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, 1, and 2 3. 2, are also like terms. Like Terms Unlike Terms w and w 5 and 1. 8 7 5 x 2 and 2 x 6 a and 6 b 3. 2 and n The exponents The variables Only one term contains a are different variable 3 x and 2 x

Simplifying Algebraic Expressions Additional Example 1: Identifying Like Terms Identify like terms in the list. 3 t 5 w 2 7 t 9 v 4 w 2 8 v Look for like variables with like powers. 3 t 5 w 2 7 t 9 v Like terms: 3 t and 7 t 4 w 2 8 v 5 w 2 and 4 w 2 9 v and 8 v Helpful Hint Use different shapes or colors to indicate sets of like terms.

Simplifying Algebraic Expressions Check It Out: Example 1 Identify like terms in the list. 2 x 4 y 3 8 x 5 z 5 y 3 8 z Look for like variables with like powers. 2 x 4 y 3 8 x 5 z Like terms: 2 x and 8 x 5 y 3 8 z 4 y 3 and 5 y 3 5 z and 8 z

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

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

Simplifying Algebraic Expressions Additional Example 2: Simplifying Algebraic Expressions Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. C. 3 a 2 + 5 b + 11 b 2 – 4 b + 2 a 2 – 6 (3 a 2 + 2 a 2) + (5 b – 4 b) + 11 b 2 – 6 5 a 2 + b + 11 b 2 – 6 Identify like terms. Group like terms. Add or subtract the coefficients.

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

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

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

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

Simplifying Algebraic Expressions Lesson Quizzes Standard Lesson Quiz for Student Response Systems

Simplifying Algebraic Expressions Lesson Quiz: Part I Identify like terms in the list. 1. 3 n 2 5 n 2 n 3 8 n 2. a 5 2 a 2 a 3 3 a 4 a 2 5 n, 8 n 2 a 2, 4 a 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. 3. 4 a + 3 b + 2 a 4. x 2 + 2 y + 8 x 2 6 a + 3 b 9 x 2 + 2 y

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

Simplifying Algebraic Expressions Lesson Quiz for Student Response Systems 1. Identify the like terms in the list. 6 a, 5 a 2, 2 a, 6 a 3, 7 a A. 6 a and 2 a B. 6 a, 5 a 2, and 6 a 3 C. 6 a, 2 a, and 7 a D. 5 a 2 and 6 a 3

Simplifying Algebraic Expressions Lesson Quiz for Student Response Systems 2. Identify the like terms in the list. 16 y 6, 2 y 5, 4 y 2, 10 y, 16 y 2 A. 16 y 6 and 16 y 2 B. 4 y 2 and 16 y 2 C. 16 y 6 and 2 y 2 D. 2 y 5 and 10 y

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

Simplifying Algebraic Expressions Lesson Quiz for Student Response Systems C. 5 x + 2 y + 7 x = 5 x + 7 x + 2 y Commutative Property = (5 x + 7 x) + 2 y Associative Property = 12 x + 2 y Add the coefficients. D. 5 x + 2 y + 7 x = 5 x + 7 x + 2 y Associative Property = (5 x + 7 x) + 2 y Commutative Property = 12 x + 2 y Add the coefficients.

Simplifying Algebraic Expressions Lesson Quiz for Student Response Systems 4. Simplify 5 x 2 + 3 x + 8 x 2. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. A. 5 x 2 + 3 x + 8 x 2 = 5 x 2 + 8 x 2 + 3 x Associative Property = (5 x 2 + 8 x 2) + 3 x Commutative Property = 13 x 2 + 3 x Add the coefficients. B. 5 x 2 + 3 x + 8 x 2 = 3 x + 5 x 2 + 8 x 2 Commutative Property = (3 x + 5 x 2) + 8 x 2 Associative Property = 8 x + 8 x 2 Add the coefficients.

Simplifying Algebraic Expressions Lesson Quiz for Student Response Systems C. 5 x 2 + 3 x + 8 x 2 = 5 x 2 + 8 x 2 + 3 x Commutative Property = (5 x 2 + 8 x 2) + 3 x Associative Property = 13 x 2 + 3 x Add the coefficients. D. 5 x 2 + 3 x + 8 x 2 = 3 x + 5 x 2 + 8 x 2 Associative Property = (3 x + 5 x 2) + 8 x 2 Commutative Property = 8 x + 8 x 2 Add the coefficients.

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