Question

select the correct answer.
what is the factored form of this expression?
x⁹ − 1,000
a. (x³ + 10)(x⁶ − 10x³ + 100)
b. (x³ − 10)(x⁶ + 10x³ + 100)
c. (x³ − 10)(x³ + 10)(x² − 10x + 100)
d. (x − 10)(x + 10)(x³ − 10x² + 100)

Explanation:

Step1: Recall Difference of Cubes Formula

The difference of cubes formula is \(a^3 - b^3=(a - b)(a^2+ab + b^2)\). Here, \(x^9=(x^3)^3\) and \(1000 = 10^3\), so the expression \(x^9 - 1000\) can be written as \((x^3)^3-10^3\).

Step2: Apply the Formula

Using the difference of cubes formula with \(a = x^3\) and \(b = 10\), we get:

$$
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$$

Answer:

B. \((x^3 - 10)(x^6 + 10x^3 + 100)\)