1 6 Simplifying Algebraic Expressions Warm up P

1 -6 Simplifying Algebraic Expressions Warm up P 26 # 3, 8, 9, 20, 25

1 -6 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

1 -6 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

1 -6 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.

1 -6 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

1 -6 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.

1 -6 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.

1 -6 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 Identify like terms. Commutative Property (3 a 2 + 2 a 2) + (5 b – 4 b) + 11 b 2 – 6 Associative Property Add or subtract the 5 a 2 + b + 11 b 2 – 6 coefficients. 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

1 -6 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.

1 -6 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. Commutative 4 x 2 + 3 x 2 + 2 x 2+ 4 y – 4 y + 5 Property 2 2 2 (4 x + 3 x + 2 x )+ (4 y – 4 y) + 5 Associative Property Add or subtract the 9 x 2 + 5 coefficients.

1 -6 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

1 -6 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

1 -6 Simplifying Algebraic Expressions Classwork P 30 # 18 -27 P 505 # 13 -35 odd