Final answer:
To multiply 2x(x^2 + 2x - 6), distribute 2x to each term inside the parentheses to obtain 2x^3 + 4x^2 - 12x.
Step-by-step explanation:
To multiply the expression 2x(x^2 + 2x - 6), we use the distributive property of multiplication over addition. We multiply each term inside the parentheses by 2x, resulting in:
2x(x^2) + 2x(2x) + 2x(-6)
We simplify each term:
2x^3 + 4x^2 - 12x
So, the correct answer is Option A) 2x^3 + 4x^2 - 12x.