Question

Which expression shows one way to rewrite x⁴-64

A. 8x²(x²-8)
B. (x²+8)(x²-8)
C. (x²+32)(x²-32)
D. (x+4)(x-4)(x²+8)

Answer 1

Answer: Option B

Step-by-step explanation:

To rewrite \(x^4 - 64\), you can use the difference of squares identity (\(a^2 - b^2 = (a + b)(a - b)\)).

\[x^4 - 64 = (x^2)^2 - 8^2\]

Now, you can apply the difference of squares:

\[x^4 - 64 = (x^2 + 8)(x^2 - 8)\]

So, the correct expression is option B: \((x^2 + 8)(x^2 - 8)\).

Answer 2

To rewrite the expression x⁴-64, use the difference of squares formula, which gives (x² + 8)(x² - 8).

Step-by-step explanation:

To rewrite the expression x⁴-64, we can use the difference of squares formula, which states that a² - b² can be factored as (a + b)(a - b). Applying this formula, we get (x² + 8)(x² - 8). Therefore, the correct answer is B. (x² + 8)(x² - 8).