I am trying to factor by grouping so I did x² - (n² + 2n - 1)
I am trying to factor the stuff in parentheses first and then after that put the x² - by it and factor the diff of squares.
However, I am stuck. I can't find the numbers that multiply to -1 and add to 2.
The answer is supposed to be x² - (n-1)² and then simplified (x+1-n)(x-n+1). How do I achieve this answer? What am I doing wrong?
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Verified answer
x² - n² + 2n - 1 = x² - (n² - 2n + 1), and NOT x² - (n² + 2n - 1), as you did
x² - (n² - 2n + 1) = x² - (n - 1)²
Using the formula a² - b² = (a + b)(a - b),
x² - (n - 1)² = (x + n - 1)(x - (n - 1)) = (x + n - 1)(x - n + 1)
n^2 - 2n + 1 = (n-1)^2, so -(n-1)^2 = -n^2 +2n - 1
x^2 = x^2
Try:
(x - (n-1))*(x + (n-1))