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Algebraic Expressions Worksheet

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Algebraic Expressions Worksheet

Algebraic expressions illustration

📚 Part 1: Identifying Components of Algebraic Expressions

1. In the expression 5x + 3y - 7, identify each component:

Variables: ________________

Coefficients: ________________

Constants: ________________

Operators: ________________

2. Which of the following represents a coefficient in the expression 4a - 2b + 9?

a

4

9

-

3. Circle all the terms in the expression below:

8m + 3n - 12 + 6m

4. How many terms are in the expression 2x² + 5x - 3y + 8?

3

4

5

6

✏️ Part 2: Translating Between Words and Algebraic Expressions

5. Translate each verbal phrase into an algebraic expression:

a) Five more than twice a number: ________________

b) The product of 7 and a number decreased by 4: ________________

c) Three times the sum of a number and 8: ________________

6. Write a verbal description for the expression 6x - 15:
7. A movie theater charges $12 per ticket plus a $3 service fee per order. Write an algebraic expression for the total cost of buying t tickets:

Expression: ________________

8. Sarah has $25 and spends $4 each day. Write an expression for how much money she has after d days:

Expression: ________________

🔧 Part 3: Simplifying Algebraic Expressions

9. Simplify each expression by combining like terms:

a) 3x + 7x - 2x = ________________

b) 5y + 3 - 2y + 8 = ________________

c) 4a + 6b - a + 2b = ________________

10. Use the distributive property to simplify: 3(2x + 4)
11. Simplify completely: 2(3x + 1) + 4x - 5
12. Real-World Application: A pizza costs $8 plus $2 for each topping. If you order p pizzas with t toppings each, write and simplify an expression for the total cost:

Original expression: ________________

Simplified expression: ________________

Explain what your expression means in your own words:

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