My Math Forum fairly basic question regarding remarkable products

 Pre-Calculus Pre-Calculus Math Forum

 April 6th, 2017, 05:39 AM #1 Newbie   Joined: Mar 2017 From: leuven Posts: 20 Thanks: 0 fairly basic question regarding remarkable products so i saw this thing in my book: x²-2x-3=0 <-> (x²-2x+1)-1-3 = 0 <-> (x-1)²-4 = 0 So i've never seen this +1-1 thing before When are you allowed to do this? It seems as if they put in the +1 to get a remarkable product, I don't know the specific rules of those but why did they do this? i saw remarkable products 5 years ago but i had some troubles back then and dropped to a lower level course where we didn't see those again. So i don't know all of the specific rules regarding remarkable products also later on they do: (x-1)²=4 x-1=2 or x-1=-2 x=3 or x=-1 Why can't they do: (x-1)²=4 x²-1²=4 x²=4-1 x=√3 This gives a completely different result. I don't know why though I want to be able to spot something like this myself so i'd really like to know why exactly this doesn't work. Last edited by vlekje5; April 6th, 2017 at 05:49 AM.
April 6th, 2017, 07:04 AM   #2
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Quote:
 Originally Posted by vlekje5 Why can't they do: (x-1)²=4 x²-1²=4 x²=4-1 x=√3
That is ENTIRELY wrong.
You need to learn the basics;
as example (x-1)^2 is NOT equal to x^2 - 1^2

 April 7th, 2017, 06:07 AM #3 Newbie   Joined: Mar 2017 From: leuven Posts: 20 Thanks: 0 yeah you're right, i did learn this in my first year of middle school but never had to use it since and forgot it. Just refreshed it using a website, makes alot more sence now. Not paying attention during math class as a kid has its downsides

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