Question
Factories 4n²-100=0
Answers
GPT-4o mini
To factor the equation \(4n^2 - 100 = 0\), we can first rewrite the equation in a simpler form.
1. Start by recognizing that \(4n^2 - 100\) can be expressed as a difference of squares:
\[
4n^2 - 100 = (2n)^2 - 10^2
\]
2. Using the difference of squares formula, \(a^2 - b^2 = (a - b)(a + b)\), we can factor it as follows:
\[
(2n - 10)(2n + 10) = 0
\]
3. Now, we can set each factor equal to zero to find the solutions:
- For \(2n - 10 = 0\):
\[
2n = 10 \quad \Rightarrow \quad n = 5
\]
- For \(2n + 10 = 0\):
\[
2n = -10 \quad \Rightarrow \quad n = -5
\]
Thus, the factored form is:
\[
(2n - 10)(2n + 10) = 0
\]
And the solutions are \(n = 5\) and \(n = -5\).
1. Start by recognizing that \(4n^2 - 100\) can be expressed as a difference of squares:
\[
4n^2 - 100 = (2n)^2 - 10^2
\]
2. Using the difference of squares formula, \(a^2 - b^2 = (a - b)(a + b)\), we can factor it as follows:
\[
(2n - 10)(2n + 10) = 0
\]
3. Now, we can set each factor equal to zero to find the solutions:
- For \(2n - 10 = 0\):
\[
2n = 10 \quad \Rightarrow \quad n = 5
\]
- For \(2n + 10 = 0\):
\[
2n = -10 \quad \Rightarrow \quad n = -5
\]
Thus, the factored form is:
\[
(2n - 10)(2n + 10) = 0
\]
And the solutions are \(n = 5\) and \(n = -5\).