Question

select the correct answer.
what is the factored form of $b^3 - 1,000$
a. $(b + 10)(b^2 - 10b + 100)$
b. $(b - 10)(b^2 + 10b + 100)$
c. $(b - 10)(10b^2 + b + 100)$
d. $(b + 10)(10b^2 - b + 100)$

Explanation:

Step1: Identify difference of cubes

Recall the difference of cubes formula: $a^3 - c^3 = (a - c)(a^2 + ac + c^2)$. Here, $b^3 - 1000 = b^3 - 10^3$, so $a = b$, $c = 10$.

Step2: Apply the formula

Substitute $a = b$ and $c = 10$ into the difference of cubes formula:
$(b - 10)(b^2 + (b)(10) + 10^2)$
Simplify the terms inside the second parentheses:
$(b - 10)(b^2 + 10b + 100)$

Answer:

B. $(b - 10)(b^2 + 10b + 100)$