Question

select the correct answer.

what is the factored form of (b^3 - 1,000)?

• ((b + 10)(b^2 - 10b + 100))
• ((b - 10)(b^2 + 10b + 100))
• ((b - 10)(10b^2 + b + 100))
• ((b + 10)(10b^2 - b + 100))

Explanation:

Identify the terms as perfect cubes

$$ b^3 - 1,000 = b^3 - 10^3 $$

Apply the difference of cubes formula

$$ x^3 - y^3 = (x - y)(x^2 + xy + y^2) $$

Substitute the values into the formula

$$
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$$

Answer:

• (A) \((b + 10)(b^2 - 10b + 100)\)
• (B) \((b - 10)(b^2 + 10b + 100)\) (Correct answer)
• (C) \((b - 10)(10b^2 + b + 100)\)
• (D) \((b + 10)(10b^2 - b + 100)\)