b) \( 8 x^{3}-1 \)

Did you know that the expression \( 8x^3 - 1 \) is actually a difference of cubes? That's right! It can be factored using the formula \( a^3 - b^3 = (a - b)(a^2 + ab + b^2) \). In this case, \( a = 2x \) and \( b = 1 \), so you can rewrite it as \( (2x - 1)((2x)^2 + 2x \cdot 1 + 1^2) \) which simplifies to \( (2x - 1)(4x^2 + 2x + 1) \). In the real world, recognizing the difference of cubes can be super helpful in algebra classes and advanced math. Whether you’re solving equations or simplifying expressions, being able to factor efficiently saves time and reduces complexity. Plus, it enhances your problem-solving skills, making things feel much more intuitive and less daunting. So next time you see a cubic expression, remember this nifty factoring trick!