Factor completely.
$27x^3+125$

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

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. Recall the formulas for factoring: For sum of cubes, use \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\), and for difference of cubes, use \(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\).
3. Express each term in the given expression as a cube of some base, i.e., write each term as \(a^3\) or \(b^3\) by identifying \(a\) and \(b\).
4. Apply the appropriate formula by substituting the values of \(a\) and \(b\) into the factored form.
5. Simplify the factors if possible, and write the final factored expression as the product of a binomial and a trinomial.