Expression Equivalents 1/20

Simplify the expression: 3x + 4x + 7.

• 7x + 7

• 12x

• x + 11

• 7x + 11

Answer explanation

To simplify the expression 3x + 4x + 7, combine like terms. The like terms are 3x and 4x, which add up to 7x. So, the simplified expression is 7x + 7. This matches the correct choice, 7x + 7.

Combine like terms: 5y - 2 + 9 - 4y.

• y + 7

• y - 7

• 14y - 2

• 1y + 7

Answer explanation

To combine like terms, we add the coefficients of y: 5y - 4y = y. Then, we combine the constants: -2 + 9 = 7. Therefore, the expression simplifies to y + 7. This matches the correct choice.

Use the distributive property to simplify: 2(a + 4).

• 2a + 8

• 2a + 4

• a + 8

• 2a^2 + 8

Answer explanation

The distributive property states that when you multiply a number by a sum, you can multiply each term inside the parentheses separately and then add the results. Applying this property to 2(a + 4), we get 2a + 8. Therefore, the correct choice is 2a + 8.

Factor the expression: x^2 + 5x + 6.

• (x + 2)(x + 3)

• (x + 1)(x + 6)

• (x - 2)(x - 3)

• (x - 1)(x - 6)

Answer explanation

The expression x^2 + 5x + 6 can be factored as (x + 2)(x + 3). This is the correct choice because it satisfies the given expression.

Simplify by combining like terms: 3a + 4b - 2a + b.

• a + 5b

• 5a + 5b

• a + 3b

• 5a + b

Answer explanation

To simplify the expression, combine the like terms. The like terms are 3a and -2a, which combine to give a. Similarly, the like terms 4b and b combine to give 5b. Therefore, the simplified expression is a + 5b.

Use the distributive property to expand: -3(2m - 4n).

• -6m + 12n

• 6m - 12n

• -6m - 12n

• 6m + 12n

Answer explanation

The distributive property states that when you multiply a number by a sum or difference, you can multiply each term separately and then add or subtract the results. Applying this property to -3(2m - 4n), we get -6m + 12n. Therefore, the correct choice is -6m + 12n.

Factor the expression completely: 3x^2 - 12x.

• 3x(x - 4)

• 3x(x + 4)

• x(3x - 12)

• x(3x + 12)

Answer explanation

To factor the expression 3x^2 - 12x, we can factor out the greatest common factor, which is 3x. This gives us 3x(x - 4). Therefore, the correct choice is 3x(x - 4).

Simplify the expression: 7(2x + 3) - 4(3x + 5).

• 2x + 1

• 14x + 21 - 12x - 20

• 2x - 1

• 14x + 1

Answer explanation

To simplify the expression, distribute the numbers and combine like terms. The correct choice, 14x + 21 - 12x - 20, results from multiplying and simplifying the given expression.

Combine like terms: 8xy - 3xy + 4x^2 - x^2.

• 5xy + 3x^2

• 5xy - 3x^2

• 8xy + 3x^2

• 5x^2 + 5xy

Answer explanation

To combine like terms, add the coefficients of the same variables. In this case, 8xy - 3xy simplifies to 5xy. Similarly, 4x^2 - x^2 simplifies to 3x^2. Therefore, the correct answer is 5xy + 3x^2.

Factor the expression: 16y^2 - 25.

• (4y + 5)(4y - 5)

• (8y + 5)(2y - 5)

• (4y^2 + 25)(4y^2 - 25)

• (16y + 25)(y - 1)

Answer explanation

To factor the expression 16y^2 - 25, we use the difference of squares formula. The correct choice is (4y + 5)(4y - 5) because when we multiply these factors, we get 16y^2 - 25.