Use factoring to write an expression that is equivalent to 25b^16-64c^2

We can write this as the difference of squares:

(5b⁸+8c) (5b⁸-8c)

To write as the difference of squares, take the square root of each term first:

√25b¹⁶ = 5b⁸; √64c² = 8c

Now we write this as a sum in one binomial and a difference in the other:

(5b⁸+8c) (5b⁸-8c)