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Simplifying Algebraic Expressions What we can and can’t do…… Vocabulary Term: Parts of an algebraic expression separated by + or Coefficient: The numerical factor of a term; the number with the variable Constant: A term without a variable Like terms: Terms that have the same variable three terms 3x + 7 + x like terms 7 is the constant because it has no variable. Terms….there are 3 4n + 2n + 9 Constant….no variable Like terms….same variable Like terms can be combined. 4n + 2n + 9 = 6n + 9 Simplifying Algebraic Expressions To simplify an algebraic expression, you may have to use properties to arrange the terms to make them easier to work with……..you may just do what you CAN……. 3 + 3 = 2(3) = 6 x + x = 2x Simplify the expression 4(6x) 4(6x) = (4·6)x = 24x Parentheses mean multiplication Associative Property Let’s try some…..include the steps! 1x + 1x + 1x ** (3 · x) · 11 x + x + x = 3x 7x + 8 + x 7x + x + 8 commutative (x · 3) · 11 Commutative x · (3 · 11) Associative Combine like (7x + x) + 8 33x or x33 ** terms 8x + 8 Three friends will pay $x each for admission to the museum, plus $1 each to view the mummy exhibit. A fourth friends will pay admission but will NOT view the mummy exhibit. The expression that models this is given. Use the distributive and commutative properties to simplify the expression. 3(x + 1) + x 3x + 3 + x commutative 3x + x + 3 4x + 3 combine like terms distributive Circle the coefficients Expression Number of terms 2 none 3 8b, 2b 5x + 7 8b + 9 - 2b 4(5)x 7p + 2p + p + 18 9r + 6s + 5s + 12 Like terms? List them 1 4 4 7 6s 5s 8b – 2b + 9 = 6b + 9 none 1p Simplified by Combining Like Terms 5x + 7 9 none 7p 2p Constant 20x 18 10p + 18 12 9r + 11s + 12 Writing Expressions forMarket Word Problems The Farmer’s The Farmer’s market sells fruit baskets. Each basket has 3 apples and 1 pear. Use “a” to represent the cost of each apple and “p” to represent the cost of each pear. Write and simplify an expression that represents the total cost of 5 baskets. 3a + p in one basket, so….. 5(3a + p) in 5 baskets 15a + 5p would represent the cost of 5 baskets. Application: Word Problems Myka’s Gift Bags Myka is making eight gift bags. In each bag she will put 5 bottles of nail polish and 2 tubes of lip gloss. Write an expression for one bag. (5p + 2g) Write an expression for 8 bags. 8(5p + 2g) Evaluate for the total of all bags. 40p + 16g Today, six friends went to the museum. All paid admission, but only four of them viewed the mummy exhibit. Write an expression using parentheses. Simplify with the distributive and commutative properties. Combine like terms. Where did these values come from?? combine like terms 4(x + 1) + 2x 4x + 4 + 2x distributive 4x + 2x + 4 commutative 6x + 4 Matching Expressions to Stories Four friends went to the museum. Two of the friends watched the video tour. The other two did not. The cost of admission was $ X. The video tour was an additional $2. Find the expression. Four friends went to a local amusement park. Three of the friends bought ride tickets for x dollars, plus a game pass for $2. The other friend bought just a ride ticket. Write and simplify an expression showing the amount of total money spent. Three people had pizza for lunch. Two more students had pizza and salads. Let x represent the pizza, and s represent the salad. 3(x + 2) + x 3x + 2(x + s) 2(x + 2) + 2x Challenge Numerical: 3 + 3 + 4 = 2(3) + 4 = 6 + 4 = 10 Algebraic: x + x + y = 2x + y This is ALL we can do!!!!! Simplifying (14y + x) + 22y Commutative = (x + 14y) + 22y Associative = x + (14y + 22y) Combine like terms Simplifying Distribute: 4(2x + y) = 8x + 4y = x + 36y Start by distributing the 4. No like terms, so we have finished! Factor and Simplify Factor: 27x + 18y 9(3)x + 9(2) y 9( 3x + 2 y ) 3x + 9y + 2x 3x + 2x + 9y 5x + 9y 7(3x + y) 12x + 8y 21x + 7y 4(3)x + 4(2)y 4(3x + 2y) What did we accomplish? • • • • • We continued working with algebraic expressions. We identified parts of the expressions. We simplified using properties. We wrote expressions for word problems. We matched problems with the expression that would “tell the story” of the problem.