Factor completely.
$27x^3+125$

• A. $(3x-5)(9x^2+15x+25)$
• B. $(3x+5)(9x^2-15x+25)$
• C. $(27x+5)(x^2+25)$
• D. $(3x+5)(x^2+5)$

Answer: (B)

Verified step by step guidance

1. Identify whether the given expression is a sum or difference of cubes. The general forms are \(a^3 + b^3\) for sum of cubes and \(a^3 - b^3\) for difference of cubes.
2. Rewrite the expression in the form \(a^3 \pm b^3\), where \(a\) and \(b\) are real numbers or algebraic expressions. This may involve recognizing perfect cubes.
3. Use the sum of cubes formula: \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\), or the difference of cubes formula: \(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\) depending on the sign in the original expression.
4. Substitute the values of \(a\) and \(b\) into the appropriate formula and write the factored form as the product of a binomial and a trinomial.
5. Simplify each part if possible, and verify your factorization by expanding the factors to check if you get the original expression.