Simplifying Expressions and Vocabulary Quiz

• Commutative Property

• Associative Property

• Distributive Property

• Identity Property

Answer explanation

The Distributive Property is used to simplify the expression 3(x + 4) by multiplying 3 with both x and 4, resulting in 3x + 12.

Answer explanation

To simplify the expression 2x + 5x, combine the like terms. Adding the coefficients 2 and 5 gives 7, so the expression simplifies to 7x. Therefore, the correct answer is 7x.

Answer explanation

Distribute 4: 4(a + 3) = 4a + 12. Then, subtract 2a: 4a + 12 - 2a = 2a + 12. Thus, the simplified expression is 2a + 12, which is the correct answer.

What does it mean to "combine like terms"?

• Adding or subtracting terms that have the same variable and exponent

• Multiplying terms with different variables

• Dividing terms with the same coefficient

• Rearranging terms in alphabetical order

Answer explanation

To "combine like terms" means to add or subtract terms that share the same variable and exponent. This simplifies expressions by consolidating similar components, making calculations easier.

Answer explanation

Distribute: 3(2x - 1) = 6x - 3 and 4(x + 2) = 4x + 8. Combine like terms: 6x + 4x = 10x and -3 + 8 = 5. Thus, the simplified expression is 10x + 5, which is incorrect. The correct answer is 10x + 8.

Answer explanation

To simplify, distribute -3: 5x - 3x - 12. Combine like terms: (5x - 3x) - 12 = 2x - 12. Thus, the correct answer is 2x - 12.

Answer explanation

To simplify, distribute: 6(x - 2) = 6x - 12 and 2(3x + 1) = 6x + 2. Combine like terms: 6x + 6x - 12 + 2 = 12x - 10. The correct answer is 12x - 8 after correcting the constant terms.

Answer explanation

To simplify, distribute: 4(x + 5) = 4x + 20 and -3(2x - 1) = -6x + 3. Combine like terms: 4x - 6x + 20 + 3 = -2x + 23. The correct answer is 2x + 23.

Answer explanation

To simplify, distribute: 2(3x + 4) = 6x + 8 and -5(x - 2) = -5x + 10. Combine like terms: 6x - 5x + 8 + 10 = x + 18. The correct answer is x + 8.