Factoring Binomials - Which Method?

• Sum of cubes

• Difference of cubes

• Difference of squares

• None of these

Answer explanation

The polynomial x^3 + 8 can be expressed as x^3 + 2^3, which fits the form of a sum of cubes, a^3 + b^3 = (a + b)(a^2 - ab + b^2). Thus, the correct choice is 'Sum of cubes'.

• Sum of cubes

• Difference of cubes

• Difference of squares

• None of these

Answer explanation

The polynomial 27x^3 - 1 can be expressed as a difference of cubes, since it follows the form a^3 - b^3, where a = 3x and b = 1. Thus, the correct choice is 'Difference of cubes'.

• Sum of cubes

• Difference of cubes

• Difference of squares

• None of these

Answer explanation

The polynomial x^2 - 16 can be expressed as (x - 4)(x + 4), which is a difference of squares. It follows the formula a^2 - b^2 = (a - b)(a + b), where a = x and b = 4.

• Sum of cubes

• Difference of cubes

• Difference of squares

• None of these

Answer explanation

The polynomial 4x^2 + 9 is a sum of a square and a constant, not fitting the forms of sum/difference of cubes or squares. Therefore, the correct choice is 'None of these'.

• Sum of cubes

• Difference of cubes

• Difference of squares

• None of these

Answer explanation

The polynomial 8x^3 + 27 can be expressed as a sum of cubes, since it follows the form a^3 + b^3, where a = 2x and b = 3. Therefore, the correct choice is 'Sum of cubes'.

Which of the following is a sum of cubes?

Answer explanation

The expression x^3 + 27 can be factored as (x + 3)(x^2 - 3x + 9), which is a sum of cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2) with a = x and b = 3.

Which of the following is a difference of cubes?

Answer explanation

The expression x^3 - 27 is a difference of cubes, as it can be factored into (x - 3)(x^2 + 3x + 9). The other options do not represent a difference of cubes.

Which of the following is a difference of squares?

Answer explanation

The expression x^2 - 25 is a difference of squares because it can be factored as (x - 5)(x + 5). The other options do not fit this form.

Which of the following is a sum of cubes?

Answer explanation

The expression 8x^3 + 1 can be rewritten as (2x)^3 + 1^3, which fits the sum of cubes formula a^3 + b^3 = (a + b)(a^2 - ab + b^2). The other options do not represent sums of cubes.

Which of the following is a difference of cubes?

Answer explanation

The expression 27x^3 - 8 is a difference of cubes, as it can be factored into (3x - 2)(9x^2 + 6x + 4). The other options do not fit the form a^3 - b^3.