4-2 Simplifying Algebraic Expressions
Identify the terms, like terms, coefficients, and constants in each expression.
1. –2a + 3a + 5b
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression –2a + 3a + 5b, the terms are –2a, 3a, 5b; the like terms
are –2a, 3a; the coefficients are –2, 3, 5; and there are no constants.
2. 2x + 3x + 4 + 4x
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 2x + 3x + 4 + 4x, the terms are 2x, 3x, 4, 4x; the like
terms are 2x, 3x, 4x; the coefficients are 2, 3, 4; and the constant is 4.
3. mn + 4m + 6n + 2mn
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression mn + 4m + 6n + 2mn the terms are mn, 4m, 6n, 2mn; the
like terms are mn, 2mn; the coefficients are 1, 4, 6, 2; and there are no constants.
4. 3a + 5b + 4 + 6a
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 3a + 5b + 4 + 6a the terms are 3a, 5b, 4, 6a; the like
terms are 3a, 6a; the coefficients are 3, 5, 6; and the constant is 4.
5. 3x + 4x + 5y
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 3x + 4x + 5y the terms are 3x, 4x, 5y; the like terms are
3x, 4x; the coefficients are 3, 4, 5; and there are no constants.
6. –4p – 6q – 5
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression –4p – 6q – 5 the terms are –4p , –6q, –5; there are no
like terms; the coefficients are –4, –6; and the constant is –5.
Simplify each expression.
7. 6x + 2x + 3
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SOLUTION: 4-2
Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants
are terms
without variables.
So, in the expression –4p – 6q – 5 the terms are –4p , –6q, –5; there are no
Simplifying
Algebraic
Expressions
like terms; the coefficients are –4, –6; and the constant is –5.
Simplify each expression.
7. 6x + 2x + 3
SOLUTION: 8. –2a + 3a + 6
SOLUTION: 9. 7x + 4 – 5x – 8
SOLUTION: 10. 5a – 2 – 3a + 7
SOLUTION: 11. –3(m – 1) + 4m + 2
SOLUTION: 12. 4a – 6 – 2(a – 1)
SOLUTION: 13. JEWELRY Marena is using a certain number of blue beads in a bracelet design. She will use 7 more red beads
than blue beads. Write an expression in simplest form that represents the total number of beads in her bracelet
design.
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SOLUTION: total number of beads = number of blue beads + number of red beads
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4-2 Simplifying Algebraic Expressions
13. JEWELRY Marena is using a certain number of blue beads in a bracelet design. She will use 7 more red beads
than blue beads. Write an expression in simplest form that represents the total number of beads in her bracelet
design.
SOLUTION: total number of beads = number of blue beads + number of red beads
Let x = number of blue beads.
Let x + 7 = number of red beads.
So, the expression 2x + 7 represents the total number of beads in Marena’s bracelet design.
14. ENTERTAINMENT Kyung bought 3 CDs that cost x dollars, 2 DVDs that cost $10; and a book that costs $15.
Write an expression in simplest form that represents the total amount that Kyung spent.
SOLUTION: total amount spent = amount spent on CDs + amount spent on DVDs + amount spent on book
Let 3x = cost of 3 CDs.
Let 2(10) = cost of 2 DVDs.
Let 15 = cost of book.
So, the expression 3x + 35 represents the total amount that Kyung spent.
Identify the terms, like terms, coefficients, and constants in each expression.
15. 3a + 2 + 3a + 7
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 3a + 2 + 3a + 7 the terms are 3a, 2, 3a, 7; the like terms
are 3a, 3a; the coefficients are 3, 3; and the constants are 2, 7.
16. 4m + 3 + m + 1
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 4m + 3 + m + 1 the terms are 4m, 3, m, 1; the like terms
are 4m, m; the coefficients are 4, 1; and the constants are 3, 1.
17. 3c + 4d + 5c + 8
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 3c + 4d + 5c + 8 the terms are 3c, 4d, 5c, 8; the like
terms are 3c, 5c; the coefficients are 3, 4, 5; and the constant is 8.
18. 7j + 11j k + k + 9
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are Page 3
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 7j + 11j k + k + 9 the terms are 7j , 11j k , k, 9; there no
like terms; the coefficients are 7, 11, 1; and the constant is 9.
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SOLUTION: 4-2
Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants
are terms
without variables.
So, in the expression 3c + 4d + 5c + 8 the terms are 3c, 4d, 5c, 8; the like
Simplifying
Algebraic
Expressions
terms are 3c, 5c; the coefficients are 3, 4, 5; and the constant is 8.
18. 7j + 11j k + k + 9
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 7j + 11j k + k + 9 the terms are 7j , 11j k , k, 9; there no
like terms; the coefficients are 7, 11, 1; and the constant is 9.
19. 4x + 4y + 4z + 4
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 4x + 4y + 4z + 4 the terms are 4x, 4y, 4z, 4; there are no
like terms; the coefficients are 4, 4, 4; and the constant is 4.
20. 3m + 3n + 2p + 4r
SOLUTION: Terms are the parts of algebraic expressions that are separated by addition or subtraction signs. Like terms are
terms that contain the same variables. Coefficients are the numerical part of a term that contains a variable, and
constants are terms without variables. So, in the expression 3m + 3n + 2p + 4r the terms are 3m, 3n, 2p , 4r; there
are no like terms; the coefficients are 3, 3, 2, 4; there are no constants.
Simplify each expression.
21. 4a + 3a
SOLUTION: 22. 9x + 2x
SOLUTION: 23. –5m + m + 5
SOLUTION: 24. 6x – x + 3
SOLUTION: 25. 7p + 3 + 4p + 5
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SOLUTION: 4-2 Simplifying Algebraic Expressions
25. 7p + 3 + 4p + 5
SOLUTION: 26. 2a + 4 + 2a + 9
SOLUTION: 27. 4a – 3b – 7a – 3b
SOLUTION: 28. –x – 2y – 8x – 2y
SOLUTION: 29. x + 5(6 + x)
SOLUTION: 30. 2a + 3(2 + a)
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31. –3(6 – 2r) – 3r
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4-2 Simplifying Algebraic Expressions
30. 2a + 3(2 + a)
SOLUTION: 31. –3(6 – 2r) – 3r
SOLUTION: 32. –2(2x – 5) – 4x
SOLUTION: For each situation write an expression in simplest form that represents the total amount.
33. FASHION Mateo has y pairs of shoes. His brother has 5 fewer pairs.
SOLUTION: total pairs of shoes = number of pairs of shoes Mateo has + number of pairs of shoes Mateo’s brother has
Let y = number of pairs of shoes Mateo has
Let y – 5 = number of pairs of shoes Mateo’s brother has
So, the expression 2y – 5 represents the total number of pairs of shoes.
34. CELL PHONES You used p minutes one month on your cell phone. The next month you used 75 fewer minutes.
SOLUTION: total minutes = minutes used in one month + minutes used in the next month
Let p = minutes used in one month.
Let p – 75 = minutes used in the next month.
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4-2 So,
Simplifying
Algebraic
Expressions
the expression
2y – 5 represents
the total number of pairs of shoes.
34. CELL PHONES You used p minutes one month on your cell phone. The next month you used 75 fewer minutes.
SOLUTION: total minutes = minutes used in one month + minutes used in the next month
Let p = minutes used in one month.
Let p – 75 = minutes used in the next month.
So, the expression 2p – 75 represents the total number of minutes used in two months.
35. SPORTS Nathan scored x points in his first basketball game. He scored three times as many points in his second
game. In his third game, he scored 6 more than the second game.
SOLUTION: total points scored = points scored in first game + points scored in second game + points scored in third game
Let x = points scored in first game.
Let 3x = points scored in second game.
Let 3x + 6 = points scored in third game.
So, the expression 7x + 6 represents the total number of points Nathan scored in his three games.
36. MONEY On Monday, Rebekah spent d dollars on lunch. She spent $0.50 more on Tuesday than she did on
Monday. On Wednesday, she spent twice as much as she did on Tuesday.
SOLUTION: total amount Rebekah spent on lunch = amount spent on Monday + amount spent on Tuesday + amount spent on
Wednesday
Let d = amount Rebekah spent on Monday
Let d + 0.50 = amount Rebekah spent on Tuesday
Let 2(d + 0.50) = amount Rebekah spent on Wednesday
So, the expression 4d + $1.50 represents the amount Rebekah spent on lunch on Monday, Tuesday, and Wednesday.
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