2 9 Combining Like Terms Warm Up Problem

2 -9 Combining Like Terms Warm Up Problem of the Day Lesson Presentation Course 2

2 -9 Combining Like Terms 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 30 6. 10 y Course 2

2 -9 Combining Like Terms Problem of the Day Emilia saved nickels, dimes, and quarters in a jar. When the jar was full, she counted the money. 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 Course 2

2 -9 Combining Like Terms Learn to combine like terms. Course 2

2 -9 Combining Insert Lesson Here Like. Title Terms Vocabulary term coefficient like terms Course 2

2 -9 Combining Like Terms In the expression 7 x + 5, 7 x and 5 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 term + 5 term – 3 y 2 + term y+ x 3 term In the term 7 x, 7 is called Coefficient 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 = 1 y. Course 2 Variable

2 -9 Combining Like Terms Term Coefficient Course 2 4 a 2 3 3 k 2 x 4. 7 t 9 4 2 3 3 1 1 4. 7 9

2 -9 Combining Like Terms 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 Course 2 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

2 -9 Combining Like Terms 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. Course 2

2 -9 Combining Insert Lesson Title Here Like Terms Try This: 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 Course 2 5 y 3 8 z 4 y 3 and 5 y 3 5 z and 8 z

2 -9 Combining Insert Lesson Title Here Like Terms 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. Course 2

2 -9 Combining Like Terms Additional Example 2 A & 2 B: Combining Like Terms Combine like terms. 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. Course 2

2 -9 Combining Like Terms Additional Example 2 C: Combining Like Terms Combine like terms. 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 Course 2 Identify like terms. Group like terms. Add or subtract the coefficients.

2 -9 Combining Insert Lesson Title Here Like Terms Try This: Example 2 A &2 B Combine like terms. A. 5 y + 3 y 8 y 5 y and 3 y are like terms. Add the coefficients. B. 23 x 2 – 13 x + 6 In this expression, there are no like terms to combine. Course 2

2 -9 Combining Insert Lesson Title Here Like Terms Try This: Example 2 C Combine like terms. 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 Course 2 Add or subtract the coefficients.

2 -9 Combining Like Terms Additional Example 3: Geometry Application Write an expression for the perimeter of the triangle shown. Combine like terms in the expression. 2 x + 3 x 3 x + 2 Write an expression using the side lengths. (x + 3 x + 2 x) + (2 + 3) Identify and group like terms. 6 x + 5 Combine like terms. x + 3 x + 2 x + 3 Course 2

2 -9 Combining Insert Lesson Title Here Like Terms Try This: Example 3 Write an expression for the perimeter of the triangle shown. Combine like terms in 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 Combine like terms. x + 2 x + 1 Course 2

2 -9 Combining Insert Lesson Like. Title Terms Here Lesson Quiz: Part 1 Identify like terms. 1. 3 n 2 5 n 2 n 3 8 n 2. a 5 2 a 2 a 3 3 a 5 n, 8 n 4 a 2 2 a 2, 4 a 2 Combine like terms. 3. 4 a + 3 b + 2 a 6 a + 3 b 4. x 2 + 2 y + 8 x 2 9 x 2 + 2 y Course 2

2 -9 Combining Insert Lesson Like. Title Terms Here Lesson Quiz: Part 2 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 Course 2