Question

Which expression correctly shows 2x⁴ - 54x factored using the difference of cubes method?

a. 2(x³ - 9)(x + 3)
b. 2(x² - 9)(x² + 3)
c. 2(x³ + 9)(x - 3)
d. 2(x³ - 9)(x - 3)

Answer 1

To factor 2x⁴ - 54x using the difference of cubes method, the expression should be rewritten as the difference of cubes, resulting in the expression 2(x³ - 9)(x - 3).

Step-by-step explanation:

To factor the expression 2x⁴ - 54x using the difference of cubes method, we need to rewrite it as the difference of cubes. The formula for factoring the difference of cubes is a³ - b³ = (a - b)(a² + ab + b²). In this case, the cube root of 2x⁴ is 2x, and the cube root of -54x is -3√(6x²). Therefore, the correct expression that shows 2x⁴ - 54x factored using the difference of cubes method is d. 2(x³ - 9)(x - 3).