Factoring Cubes Challenge

Factoring Cubes Challenge

8th Grade

13 Qs

quiz-placeholder

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Factoring Cubes Challenge

Factoring Cubes Challenge

Assessment

Quiz

Mathematics

8th Grade

Practice Problem

Hard

CCSS
HSA.APR.C.4

Standards-aligned

Created by

Christian Dave Remando

Used 4+ times

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13 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

2 mins • 3 pts

Factor the expression: x^3 + 27

(x + 9)(x^2 - 9x + 81)

(x + 3)(x^2 - 3x + 9)

(x - 3)(x^2 + 3x + 9)

(x + 1)(x^2 + 1)

Answer explanation

The expression x^3 + 27 is a sum of cubes, which factors as (x + 3)(x^2 - 3x + 9). This matches the correct choice, confirming that (x + 3)(x^2 - 3x + 9) is the valid factorization.

Tags

CCSS.HSA.APR.C.4

2.

MULTIPLE CHOICE QUESTION

2 mins • 3 pts

Factor the expression: 8y^3 - 1

(2y + 1)(4y^2 - 2y + 1)

(8y - 1)(y^2 + 1)

(4y - 1)(2y^2 + 2y + 1)

(2y - 1)(4y^2 + 2y + 1)

Answer explanation

To factor 8y^3 - 1, recognize it as a difference of cubes: (2y)^3 - 1^3. Using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2), we get (2y - 1)(4y^2 + 2y + 1), which matches the correct choice.

Tags

CCSS.HSA.APR.C.4

3.

MULTIPLE CHOICE QUESTION

2 mins • 3 pts

Factor the expression: a^3 + 64

(a + 4)(a^2 - 4a + 16)

(a + 4)(a^2 + 4a + 16)

(a + 8)(a^2 - 8a + 16)

(a + 2)(a^2 - 2a + 32)

Answer explanation

The expression a^3 + 64 is a sum of cubes, which factors as (a + 4)(a^2 - 4a + 16). This matches the correct choice, as it follows the formula a^3 + b^3 = (a + b)(a^2 - ab + b^2) with a = a and b = 4.

Tags

CCSS.HSA.APR.C.4

4.

MULTIPLE CHOICE QUESTION

2 mins • 3 pts

Factor the expression: 125 - b^3

(5 - b)(25 + 5b + b^2)

(5 + b)(25 + 5b - b^2)

(5 - b)(25 - 5b + b^2)

(5 + b)(25 - 5b + b^2)

Answer explanation

The expression 125 - b^3 is a difference of cubes, which factors as (a - b)(a^2 + ab + b^2) where a = 5 and b = b. Thus, it factors to (5 - b)(25 + 5b + b^2), making this the correct choice.

Tags

CCSS.HSA.APR.C.4

5.

MULTIPLE CHOICE QUESTION

2 mins • 3 pts

Factor the expression: 27x^3 + 1

(3x - 1)(9x^2 + 3x + 1)

(27x + 1)(x^2 - 1)

(9x + 3)(3x^2 - 1)

(3x + 1)(9x^2 - 3x + 1)

Answer explanation

To factor 27x^3 + 1, recognize it as a sum of cubes: (3x)^3 + 1^3. Using the formula a^3 + b^3 = (a + b)(a^2 - ab + b^2), we get (3x + 1)(9x^2 - 3x + 1). Thus, the correct choice is (3x + 1)(9x^2 - 3x + 1).

Tags

CCSS.HSA.APR.C.4

6.

MULTIPLE CHOICE QUESTION

2 mins • 3 pts

Factor the expression: 64y^3 - 8

4(4y^3 - 2)

16(4y^3 - 1)

8(2y - 1)(4y^2 + 2y + 1)

8(2y + 1)(4y^2 - 2y + 1)

Answer explanation

To factor 64y^3 - 8, recognize it as a difference of cubes: (4y)^3 - 2^3. This factors to (4y - 2)(16y^2 + 8y + 4). Further simplifying gives 8(2y - 1)(4y^2 + 2y + 1), which is the correct choice.

Tags

CCSS.HSA.APR.C.4

7.

MULTIPLE CHOICE QUESTION

2 mins • 3 pts

Factor the expression: m^3 + 1

(m + 1)(m^2 - m + 1)

(m + 2)(m^2 - 2m + 4)

(m^3 - 1)(m + 1)

(m - 1)(m^2 + m + 1)

Answer explanation

To factor m^3 + 1, we use the sum of cubes formula: a^3 + b^3 = (a + b)(a^2 - ab + b^2). Here, a = m and b = 1, giving us (m + 1)(m^2 - m + 1) as the correct factorization.

Tags

CCSS.HSA.APR.C.4

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