Factoring x^2+4 vs. x^4+4

Factoring x^2+4 vs. x^4+4

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bprp #fast

[bprpfast]

Are there any problems that you want me to do in minute?

Let me know!

[jaymesvillafuerte]

Is no one gonna talk about how flawlessly he switches between his 2 markers.

[darkalpha]

Me after watching bprp's videos :- *My whole life was a lie!.*

[ospreytalon]

The general form of this (with 4y^4 instead of 4) is the Sophie Germain Identity, which is very useful in contests.

[trashymcgee]

I’m going to pretend I completely understand

[thedoublehelix]

x^2+4 = (x+2i)(x-2i) hah. Also, you should derive the equation for integrating a curve in polar coordinates next!

[Birendra]

x² + 1
= x² + 2x + 1 - 2x
= (x + 1)² - (√(2x))²
= {x + √(2x) + 1}{x - √(2x) +1}

It's absolutely factorisable with real numbers !

[narutonextgenerations-boru]

I'll give you 5 seconds
*Blink
Right times up

[learnwithburhan]

Easy way to solve *x⁴+4*

x⁴+4
=(x²)²+(2)²
_This is in the form of a²+b²_
=(x²)²+(2)²+2(x²)(2)-4x²
_Making it a perfect square by adding and subtracting 2ab_
=(x²+2)²-(2x)²
_Since a²+b²+2ab=(a+b)²_
=(x²+2+2x)(x²+2-2x)
_Since a²-b²=(a+b)(a-b)_

[i_saidmeow]

I love how in every video holds something on the opposite hand. Also his beard grows faster than the algorithm

[damianpantucci]

I literally teach math for a living and I still had to watch this 3 times to understand the steps

[carameldotzip]

SAYS THE PERSON WHO FACTORED 1 ACROSS THE COMPLEX NUMBERS JUST LAST WEEK.
haha love your videos.

[jkwong]

I like how u cover the mic as a pokéball :D

[soheib]

When this dude tells me dont try I wont even think about it

[emmalance]

Nice! I used complex solutions to find the real factorization.

[sohamparmar]

It's simply called perfect square method where MT=2√FT×√LT

[KCKaranChoudhary]

bprp fast,
Make short videos - nah
Fast forward - yes

[einsteingonzalez]

They’re both factorable!
Don’t you mean polynomial factors?

[brettstafford]

x^2+4
=4(1/4x^2+1)
=4((x/2)^2+1)
=4((tan(arctan(x/2)))^2+1)
=4((sec(arctan(x/2)))^2)
which can factor into
Thus x^2 + 4 is factorable

[ryzenandrewgarcia]

My take: Ain't x^2 + 4 can be factorable by real numbers, using two factoring methods like CMF (Common Monomial Factoring) and the Polynomial Factoring Method (like what you said):

=> x^2 + 4
=> x^2 + 4x + 4 - (4x)

(x^2 + 4x + 4) is a perfect square polynomial therefore:

=> (x + 2)(x + 2) - 4x
=> (x + 2)^2 - 4x

Then CMF on 4x:

=> (x + 2)^2 - 2(2x)