Using the Distributive Property

Simplify the expression: -6(a + 8).

• -6a - 48

• -6a + 48

• 6a - 48

• 6a + 48

Answer explanation

To simplify -6(a + 8), distribute -6: -6 * a = -6a and -6 * 8 = -48. Combine these results to get -6a - 48, which matches the correct answer choice.

Simplify the expression: 4(1 + 9x).

• 4 + 36x

• 4 + 9x

• 36x + 1

• 4x + 9

Answer explanation

To simplify 4(1 + 9x), distribute 4 to both terms inside the parentheses: 4 * 1 = 4 and 4 * 9x = 36x. Thus, the expression simplifies to 4 + 36x, which matches the correct answer choice.

Simplify the expression: (9m + 10) · 2.

• 18m + 20

• 9m + 20

• 18m + 10

• 9m + 10

Answer explanation

To simplify (9m + 10) · 2, distribute 2 to both terms: 2 · 9m = 18m and 2 · 10 = 20. Thus, the expression simplifies to 18m + 20, which is the correct answer.

Match the following expressions with their simplified forms.

• (4 - 3n) · 8

• 32 - 24n

• (4 + 3n) · 8

• -32 - 24n

• (-4 - 3n) · -8

• 32 + 24n

• (-4 + 3n) · -8

• -32 + 24n

Simplify the expression: 8(-b - 4).

• -8b - 32

• 8b + 32

• -8b + 32

• 8b - 32

Answer explanation

To simplify 8(-b - 4), distribute 8: 8 * -b = -8b and 8 * -4 = -32. Combine these to get -8b - 32, which matches the correct answer choice.

Simplify the expression: (1 - 7n) · 5.

• 5 - 35n

• 5 - 7n

• 5n - 35

• -35n + 1

Answer explanation

To simplify (1 - 7n) · 5, distribute 5: 1·5 - 7n·5 = 5 - 35n. Thus, the correct answer is 5 - 35n.

Simplify the expression: -6(x + 4).

• -6x - 24

• -6x + 24

• 6x - 24

• 6x + 24

Answer explanation

To simplify -6(x + 4), distribute -6 to both terms: -6 * x = -6x and -6 * 4 = -24. Combining these gives -6x - 24, which matches the correct answer choice.

Simplify the expression: 5(b - 1).

• 5b - 5

• 5b + 5

• 5b

• b - 5

Answer explanation

To simplify 5(b - 1), distribute 5 to both terms inside the parentheses: 5 * b - 5 * 1, which results in 5b - 5. Thus, the correct answer is 5b - 5.

Simplify the expression: (x + 9) · 5.

• 5x + 45

• 5x + 9

• x + 45

• 5(x + 9)

Answer explanation

To simplify (x + 9) · 5, distribute 5 to both terms: 5 · x + 5 · 9 = 5x + 45. Thus, the correct answer is 5x + 45.

Simplify the expression: -4(-8x - 8).

• 32x + 32

• 32x - 32

• -32x + 32

• -32x - 32

Answer explanation

To simplify -4(-8x - 8), distribute -4: -4 * -8x = 32x and -4 * -8 = 32. Combining these gives 32x + 32, which matches the correct answer.