Final answer:
The equivalent expression for the algebraic expression 4x^3 + 8x^2 - 12x, using the distributive property, is 4x(x^2 + 2x - 3).
Step-by-step explanation:
According to the distributive property, in the algebraic expression 4x^3 + 8x^2 - 12x, we can factor out the greatest common factor from each term. The equivalent expression can be found by identifying the common factor in each term and factoring it out. Here, the common factor is 4x. Thus, we factor 4x out from each term to get:
4x(x^2 + 2x - 3).
Using the distributive property, if we were to expand this back out, we would arrive at the original expression, confirming the equivalence of the two expressions.