QuestionDecember 17, 2025

38. Use polynomial identities to factor. -27x^3+125

38. Use polynomial identities to factor. -27x^3+125
38. Use polynomial identities to factor.
-27x^3+125

Solution
4.1(223 votes)

Answer

(3x - 5)(9x^2 + 15x + 25) Explanation 1. Identify the form -27x^3 + 125 is a sum of cubes: -(27x^3) + (125) = -(3x)^3 + (5)^3. 2. Apply sum/difference of cubes formula Use a^3 - b^3 = (a-b)(a^2 + ab + b^2) with a = 3x, b = 5. 3. Substitute and simplify (3x - 5)((3x)^2 + (3x)(5) + (5)^2) = (3x - 5)(9x^2 + 15x + 25).

Explanation

1. Identify the form<br /> $-27x^3 + 125$ is a sum of cubes: $-(27x^3) + (125) = -(3x)^3 + (5)^3$.<br />2. Apply sum/difference of cubes formula<br /> Use $a^3 - b^3 = (a-b)(a^2 + ab + b^2)$ with $a = 3x$, $b = 5$.<br />3. Substitute and simplify<br /> $(3x - 5)((3x)^2 + (3x)(5) + (5)^2) = (3x - 5)(9x^2 + 15x + 25)$.
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