32n2-2
factor 2 out
2(16n^2 -1)
The second term is a difference of two squares.
To factor the expression 32n^2 - 2, you can first factor out the common factor of 2. This gives you:
2(16n^2 - 1)
Then, you can look at the expression inside the parentheses, 16n^2 - 1. This is a special case known as a difference of two squares. In this case, the two terms are 16n^2 and 1, and their signs are different.
To factor a difference of two squares, you can use the formula:
a^2 - b^2 = (a + b)(a - b)
In our case, a = 4n and b = 1. So, we have:
16n^2 - 1 = (4n + 1)(4n - 1)
Combining this with the common factor of 2 that we factored out earlier, we get the fully factored expression:
32n^2 - 2 = 2(4n + 1)(4n - 1)