Factoring, Algebra
There are two questions :v

Step-by-step explanation:

One

v^2 - 16

This formation is called the difference of squares. That's because there are 2 squares v^2 and 16. The key to this question is the minus sign.

The square root of v^2 = v

The square root of 16 = 4

You get (v + 4)(v - 4)

Let's see what happens when you expand it.

Look what happens when you add these 4 terms together.

is what is left. The two middle terms cancel out.

Two

This one is a perfect square

w^2 + 16w + 64

(w + 8)(w + 8)

Notice both factors are the same. You might wonder how I new that.

w^2 is a perfect square so take the square root.     v      

64 is a perfect square so take the square root        8

Now you have to work backwards to see if it is right.

Adding you get w^2 + 16w + 64 which is what you started with.