Answer:
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.
- v*v = v^2
- v*(-4) = - 4v
- v*(4) = 4v
- 4*-4 = - 16
Look what happens when you add these 4 terms together.
- v^2 - 4v + 4v - 16
- v^2 - 16
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.
- w*w = w^2
- w*8 = 8w
- 8*w = 8w
- 8^2 = 64
Adding you get w^2 + 16w + 64 which is what you started with.
