Why is (n-1)(n+1)=n^2-1?

08.06.2025 00:17

Why is (n-1)(n+1)=n^2-1?

Move the nub up to the top:

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The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2

Gun owners, imagine if an attacker comes to your home and takes your gun to use against you before you had the chance to pick it up. Would you regret owning a gun?

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n^2 - 1

Scientists Fear a Passing Star Could Fling Earth Out of the Sun's Orbit, Into the Frigid Expanse Beyond - futurism.com

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So, that’s a rectangle with sides 2 and 4.

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What to know about nerve pain and tingling hands and feet - The Washington Post

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The basic answer is that you cross-multiply the values in each factor:

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Why did Donald Trump and Melania Trump sleep in different rooms?

If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2

And you are left with almost a square. One less than the square of side n.

n^2 - n + n - 1

What does it mean when I have a dream where my friend died? I had this dream last night where one of my friends died in a shootout and I woke up crying.

(n - 1)(n + 1)