Factor the difference of perfect cubes completely. 27a³ - 1000 A) (3a + 10)(9a² - 100) B) (3a - 10)(9a² + 100) C) (3a + 10)(9a² - 30a + 100) D) (3a - 10)(9a² + 30a + 100)

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Quizplus · Accepted Answer

The difference of perfect cubes can be factored using the formula $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. Here, $27a^3 = (3a)^3$ and $1000 = 10^3$, so the factorization is $(3a - 10)((3a)^2 + 3a*10 + 10^2)$, which simplifies to $(3a - 10)(9a^2 + 30a + 100)$.

Factor the Difference of Perfect Cubes Completely