Question
Factories 4n²-100
Answers
GPT-4o mini
To factor the expression \(4n^2 - 100\), we can notice that it is a difference of squares. The expression can be rewritten as:
\[
4n^2 - 100 = (2n)^2 - 10^2
\]
This fits the difference of squares formula \(a^2 - b^2 = (a - b)(a + b)\), where \(a = 2n\) and \(b = 10\). Applying the formula, we get:
\[
4n^2 - 100 = (2n - 10)(2n + 10)
\]
We can further factor \(2n - 10\) and \(2n + 10\):
\[
2n - 10 = 2(n - 5)
\]
\[
2n + 10 = 2(n + 5)
\]
Thus, we can factor \(4n^2 - 100\) fully as:
\[
4n^2 - 100 = 2(n - 5) \cdot 2(n + 5) = 4(n - 5)(n + 5)
\]
So the fully factored form of \(4n^2 - 100\) is:
\[
4(n - 5)(n + 5)
\]
\[
4n^2 - 100 = (2n)^2 - 10^2
\]
This fits the difference of squares formula \(a^2 - b^2 = (a - b)(a + b)\), where \(a = 2n\) and \(b = 10\). Applying the formula, we get:
\[
4n^2 - 100 = (2n - 10)(2n + 10)
\]
We can further factor \(2n - 10\) and \(2n + 10\):
\[
2n - 10 = 2(n - 5)
\]
\[
2n + 10 = 2(n + 5)
\]
Thus, we can factor \(4n^2 - 100\) fully as:
\[
4n^2 - 100 = 2(n - 5) \cdot 2(n + 5) = 4(n - 5)(n + 5)
\]
So the fully factored form of \(4n^2 - 100\) is:
\[
4(n - 5)(n + 5)
\]