Factor completely. Remember to look first for a common factor. If a polynomial is prime, state this

-4t^2 + 64

this is the difference of two squares

a^2-b^2 = (a+b)(a-b)

64 - 4t^2 = 4(16-t^2) = 4 (4+t)(4-t)

To factor the given expression, -4t^2 + 64, let's first check for a common factor among both terms. In this case, -4t^2 and 64 do not share a common factor other than 1.

Next, let's factor out the greatest common factor from the expression, which in this case is -4. Factoring out -4 gives us:

-4(t^2 - 16)

Now, let's focus on the expression inside the parentheses, t^2 - 16. This is a difference of squares because it can be written as (t)^2 - (4)^2. The difference of squares formula is:

a^2 - b^2 = (a + b)(a - b)

Using this formula, we can rewrite t^2 - 16 as (t + 4)(t - 4).

Putting it all together, the completely factored form of -4t^2 + 64 is:

-4(t + 4)(t - 4)