Factor the sum or difference of two cubes.
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Question

Quizplus · Accepted Answer

The sum or difference of two cubes is factored using the formulas:
a³ + b³ = (a + b)(a² - ab + b²)
a³ - b³ = (a - b)(a² + ab + b²)
In this case, we cannot apply the formula for (a + b)(a² - ab + b²) because there is only one term being cubed. However, we can rewrite the expression as follows:
(2y³ + 1) - (y²)³
Now, we can apply the formula for a³ - b³ with a = 2y and b = y²:
a³ - b³ = (a - b)(a² + ab + b²)
(2y)³ - (y²)³ = (2y - y²)(4y² + 2y(y²) + (y²)²)
= (y²(2 - y))(4y² + 2y³ + y⁴)
= (y² - y³)(4y² + 2y³ + y⁴)
Therefore, the correct answer is C.

Factor the Sum or Difference of Two Cubes