Which expression is equivalent to 2t^3-16 ? A (2t-4)(t^2+8t+2) B 2(t-8)(t+8) C (2t+4)(t^2-4) D 2(t-2)(t^2+2t+4)

To determine which expression is equivalent to $2t^3 - 16$, we need to factor the polynomial.

First, let's factor out the greatest common factor (GCF) from the polynomial:
$$2t^3 - 16 = 2(t^3 - 8)$$

Next, we recognize that $t^3 - 8$ is a difference of cubes. The difference of cubes formula is:
$$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$

In this case, $a = t$ and $b = 2$. Applying the formula:
$$t^3 - 8 = (t - 2)(t^2 + 2t + 4)$$

So, we have:
$$2(t^3 - 8) = 2(t - 2)(t^2 + 2t + 4)$$

Thus, the expression equivalent to $2t^3 - 16$ is:
$$2(t - 2)(t^2 + 2t + 4)$$

Therefore, the correct answer is:
D $2(t-2)(t^{2}+2t+4)$