Expressions and Like Terms: Mastering Distributive Property

1. Sarah is buying 3 packs of pencils. Each pack contains 'x' pencils. Write an expression for the total number of pencils she buys using the distributive property.

• 4x

• 3x

• x + 3

• 2x

2. A store sells 'y' shirts for $15 each and 'y' pairs of pants for $25 each. Write an expression for the total cost of buying 'y' shirts and 'y' pants, then simplify it by combining like terms.

• 40y

• 30y

• 25y

• 15y

3. If a rectangle has a length of 'x + 3' and a width of 'x - 2', use the distributive property to write an expression for the area of the rectangle.

• 2x + 1

• x^2 - x + 6

• x^2 + 5x - 6

• x^2 + x - 6

4. A gardener is planting 'x' rows of flowers. Each row has '3x + 2' flowers. Write an expression for the total number of flowers and simplify it by combining like terms.

• 3x^2 + 2x

• 3x^2 + 5x

• 4x^2 + 2

• 2x^2 + 3x

6. A car rental company charges a flat fee of $50 plus $20 for each day rented. Write an expression for the total cost of renting a car for 'd' days and simplify it using the distributive property.

• 50d + 20

• 20d + 50

• 50 + 10d

• 50 + 20d

7. A school is organizing a field trip for 'x' students. The cost per student is $10 and there is a $50 bus fee. Write an expression for the total cost and simplify it by combining like terms.

• 5x + 50

• 10x + 100

• 10x - 50

• 10x + 50

8. A box contains 'x' toys, and each toy costs $5. Write an expression for the total cost of the toys and factor it.

• 5x

• x/5

• 5x + 5

• $10x

9. A pizza place sells 'x' large pizzas for $12 each and 'x' small pizzas for $8 each. Write an expression for the total cost of the pizzas and simplify it by combining like terms.

• 22x

• 18x

• 15x

• 20x

10. A farmer has 'x' apple trees and each tree produces '4x + 6' apples. Write an expression for the total number of apples produced and factor the expression.

• 8x^2 + 12

• 2x(2x + 3)

• x(4x + 6)

• 4x^2 + 6x