Evaluate the following expression if `a=8`, `b=16`, `c=-4`.

`a^{2}+2bc+3`

To evaluate the expression `a^{2}+2bc+3` with `a=8`, `b=16`, and `c=-4`, we substitute the values into the expression:

`8^{2} + 2(16)(-4) + 3`

First, we simplify the exponent:

64 + 2(16)(-4) + 3

Next, we simplify the multiplication:

64 + 2(-64) + 3

Now, we perform the multiplication:

64 - 128 + 3

Finally, we add and subtract:

-64 + 67

The expression evaluates to 3.