Factor the expression k to the second power +16+64

I'm pretty sure you mean k² + 16k + 64.  If we simplified k² + 16 + 64 to k² + 80, that expression wouldn't be factorable.  This is how k² + 16k + 64 would be factored:

k² + 16k + 64
(k + 8)(k + 8)  or  (k + 8)²

To test if this is correct factoring, simply multiply the terms back together and see if you end up with your original expression.  Use FOIL -- First, Outside, Inside, Last -- multiplication (see attached picture):

(k + 8)(k + 8)

k² + 8k + 8k + 64

k² + 16k + 64

Check!  The factored form of the expression k² + 16k + 64 is (k + 8)(k + 8) or (k + 8)².

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