Final answer:
The given expression 2x²y + 8x²y + 6xy simplifies to 16x²y after factoring, meaning none of the provided answer choices are correct.
Step-by-step explanation:
To completely factor the expression 2x²y + 8x²y + 6xy, we identify the common factors in each term. The expression breaks down into 2xy(x + 4x + 3). However, x is common in all of the terms inside the parentheses, so we can also factor out x to simplify further: 2x²y(1 + 4 + 3). Simplifying the terms within the parentheses, we get 2x²y(1 + 4 + 3) = 2x²y(8). The most factored form, combining like terms, is actually 2x²y(1 + 4 + 3) = 16x²y. Therefore, none of the choices a, b, c, or d are correct.