Question

what is \\(64x^{12} - 1,000\\) written as a difference of cubes?

\\((4x)^3 - 10^3\\)
\\((8x)^3 - 100^3\\)
\\((4x^4)^3 - 10^3\\)
\\((8x^4)^3 - 100^3\\)

Explanation:

Identify the cube root of the first term

$$ \sqrt[3]{64x^{12}} = \sqrt[3]{64} \cdot \sqrt[3]{x^{12}} = 4x^4 $$

Identify the cube root of the second term

$$ \sqrt[3]{1000} = 10 $$

Write as a difference of cubes

$$ 64x^{12} - 1000 = (4x^4)^3 - 10^3 $$

Answer:

• (A) \((4x)^3 - 10^3\)
• (B) \((8x)^3 - 100^3\)
• (C) \((4x^4)^3 - 10^3\) (Correct answer)
• (D) \((8x^4)^3 - 100^3\)