Date _ - - Reteaching with Practice ~ For use with pages 16-23 (Slim Simplify algebraic expressions. Vocabulary In an expression that can be written as a sum, the parts added together are called the terms. When a term is a product of a number and a power of a variable, the number is called the coefficient of the power. Like terms have the same variable parts. If a term has a number part but no variable part, it is called a constant term. An expression in which all grouping symbols are removed and all like terms are combined is a simplified expression. Jf£tMIQ!11 Identify coefficients and like terms Identify theccefflclents and like terms in the expression 2x - 4Xl + 5 - 7 Xl - 3 + 9x. Solution Begin by writing the expression as a sum in order to identify the terms. + 9x = 2x + (-4x 2) + 5 + (-7x 2) + (-3) + 9x 2x - 4x 2 + 5 - 7x 2 - 3 :> co CtJ 0.. The coefficients ofthe expression are 2, -4, -7, and 9. The terms 2x and 9x are like terms. The terms -4x2 and -7x2 are also like terms. The terms Q_ ""...'1- ..... Cf 1- 5 and - 3 are also like terms. Exercises for Example 1 . .- ,rl? Loe.f-f: .--/ 1. ~-7-3x2+~.~/ 3. - 3t + 8t 2 + 8t + 9 + 4t 2 C~<.;..i;.'i,+../ : - 3"'-'b" b L:=- ~u . .' I { I _ ~) E a U 7 (£,; r"-p ,; t=i eel) co - 3/ LI .8 LoeAr . .. <'&'1 II - '3>, ...;6y2 + 7y - 8 - 3y2 + 5y ,"=. ---==- 4. l2w - 5w + 3 + + 3w - 7 2. 8w I .c Q) ::> a ::r:: '+ a co a 'iii :2: -0 CtJ Simplify by combining like terms -6(y - 2) co + 4(y - 1) = -6y + 12 + 4y - 4 OJ t:' Distributive property ~ CtJ Q) ::> = (-6y + 4y) + (12 - 4) = -2y + 8 a Group like terms. Cl Combine like terms. .0 ~ > @ ..... x: ,S" Exercises for Example 2 > 0.. a U Simplify by combining like terms. 5. 3t + 5t 2 - 2t + 6t 2 7. -4(m - 2) + 3(m + 1) _ Ltm t- e t- 3 tl'/ r 3 \--:=- V1,,,--:;--j-'1 32 t Algebra 2 Concepts and Skills Chapter 1 Resource Book ..----------- + 5q + 14 6. 7(q - 2) 8. 2 2) 8d, + 2d ~ 3(d +. d _ J.2 8"c-l. t 2tt - 3d - :-SC\ C=d-Z;5~ll Date Reteaching with Practice ~~~--' _ ~ continued Foruse with pages 16-23 Imm!1:1 Simplify expressions with grouping symbols Simplify the expression 2x + 5(3x 7). Solution 2x + 5(3x - 7) = 2x = (2x + 15x 35 + Distributive property 15x) 35 Group like terms. = 17x 35 Combine like terms. (j)30'1 - uc + ~ 'I ?> 3'y- Lto r.,» ...,,' -.-r--" ~ <,'7, c> "" ~j ~Hl r: '1 Exercises for Example 3 Simplify the expression. , 9. + 3y 5(6y - 8) r • .- 10. 11.4(-5n-7)+3(3n-9) 12. 7h - 2(5h , 5 + 4) -6(4d-2)-4(2d+8) -'v,--td iImiI~!1:1 - , --, =-1/r1- 5 I Simplify a mathematical model '-"5'd -3..:J. -3 ..L d '-2_0 t /2. The width of a rectangular patio is n + 3 and the length of the patio is 7 n. Write and simplify an expression that represents the perimeter of the patio. Then find the perimeter if n = 2 feet. Solution Write a verbal model. Then write an algebraic expression. Number of sides Width (in feet) ~ ~ (n 2 '0 c; a '0 ~ + 7n 2 An algebraic expression for the perimeter is P = 2(n '(;; :~ + 3) 2(n + 3) + 2(7n) = 2n = (2n co = When n + 6 + 14n + 14n) + 6 16n + 6 Group like terms. Combine like terms. = 2, the perimeter is 16(2) + 6 = 32 + 6 = 38 feet. @ 13. . eo:: e ::: _ 2-( J. ( ;l. n -\" 3/ -+ 5 n) I-b', +- {; + \0 ~I -t/' 1,"* Y1 -t-(:, The width of a rectangular patio is 2n + 3 and the length of the patio is 5n. Write and simplify an expression that represents the perimeter ofthe patio. Then find the perimeter if n = 4 feet. t..\- (y--') ;-6 &. 2 ~: eCi" r:;. \ 14. + 3) + 2(7n). Distributive property Exercises for Example 4 ) Length (in feet) Number of sides + e .: You purchase 12 packages of wrapping paper. Large packages cost $7 and small packages cost,$4.50. Write and simplify an expression that represents the total cost if n of the 12 packages are large packages. Then find the total cost if 8 of the 12yackages ar~~arge packa~~s. ~ 1'S (f;) S'-\- ::$. ~ In v/ n + t- 4. S ( (2-- tI ) -I- SLf - Y ~ iSh I ~. n +-'51f '7tf Algebra 2 Concepts and Skills Chapter 1Resource Book 33 Name _ Date _ _ _ Practice A ~ Foruse with pages 16-23 Identify the terms in the expression. 1. 3w - 10 3. - 9n + 14 - 3n2 +9 2. 8d 2 4. 8 + 7r - 9,-2 - 3d Identify the coefficients and like terms in the expression. 5. Y+ 7. l5t - lOt2 + 6t - 9 + 2f2 6 - 5y + lOy 6. -6x + 7x 2 8. 4m + 7 - 8m - 9 - 5 + 8x Simplify the expression by combining like terms. -4n + 9n 10. 8x - lOx 11. -9m + 3 + 7m 12. 17d - lId - 8 13. 12 - 9z + 6 14. 15 - 8p - 9 + 2p 15. -9y + lOy 2 + 5y + 2y 2 16. 8n2 + 7n - 9n2 9. + 9b2 17. b' - b - - l8n 7b Simplify the expression. 18. -3(v-2)+5v 19. 8 + 5([ + 4) 20. -(q + 6) + 4q 21. 2(6t - 9) + 5(2t+ 1) 23. 5(2c - 1) - 8c 22. -7(2h - 4) 24. 7(3w 2 26. - + 6(3h - 8) 4w) - 5(w2 - w) > c:: co a. E o co 25. 5(,-2 + r) - 3(,-2 - 2r) ,0= ~ ~ c:: 5 - 2(2.5a + 7) .8 ..c: 27. Cl ::::l Tips You work with 6 other people at an ice cream stand. At the end of the night, o :r: you divide the tips evenly. Write an expression to show how much each person receives. If the tips equal $110.70, how much does each person get? '+ o c; ,,=, tn :~ 28. '0 Tickets You and some friends are going to a concert. Tickets cost $20 each. There is a $4 charge to order the tickets online. Write an expression for the total cost of ordering the tickets online. Then find the total cost if you order 7 tickets. co Q) to :.::::; co Cl ::::l 29. o Bike Rental You are renting a bike. It costs $5 for a helmet and $3 per hour. Write o an expression for the total cost of renting a bike. Find the total cost if you plan to use the bike for 4 hours. > ..a ~ 9 +-' .c: Cl .~ a. o co l 30 Algebra 2 Concepts and Skills Chapter 1 Resource Book