Answer:
-4(3v - 10)(3v + 10)
Explanation:
You must find the factored form of 400 - 36v^2.
You can rearrange this to - 36v^2 + 400 to make it less confusing.
So you have - 36v^2 + 400.
The next step is to see what you can take out of this. You can take out a GCF, a greatest common factor. This is basically a number that goes into both 36 and 400. This number is 4.
36 / 4 = 9 and 400 / 4 = 100.
Since it is a negative 36, you need to take out a negative 4.
So you put a 4 outside parenthesis and divide - 36 / 4 and 400 / 4.
-4(9v^2 - 100).
Now you must factor the inside of the parenthesis.
9v^2 - 100.
This is the same as 9v^2 + 0v - 100.
What are 2 numbers that multiply to get -100 and add to get 0?
These numbers are -10 and +10.
2 terms that multiply together get 9v^2 are 3v and 3v.
So the answer is:
-4(3v - 10)(3v + 10).
This is the factored form.