what do I factor out of $$\left(\frac{1}{9}x^4+\frac{1}{4}\right)\left(\frac{1}{4}+\frac{9}{16}x^{-4}\right)$$ to get a perfect square?
#perfect square trinomial help
pliant moth
brave kilnBOT
stiff viperBOT
jarker
pliant moth
like in $(ax+b)^2$ form
stiff viperBOT
jarker
pliant moth
oh come on guys you know you wanna factor the perfect square trinomial :))))
stiff viperBOT
adonhs
pliant moth
can you walk me through the thought process. that is bs. how are you suppose to just visualize that on the spot. these math problems just skip over everything like it's second nature or something
meager kayak
can you walk me through the thought process. that is bs. how are you suppose to ...
i feel ya
sullen crystal
can you walk me through the thought process. that is bs. how are you suppose to ...
multiply it out
pliant moth
be honest, did you use an online calculator to factor it
I'm really trying to figure out how you would go about this realistically in an exam scenario.
sullen crystal
the audacity lol
pliant moth
you seriously converted the whole equation to that form in your head then. Like no shame just want to know how you did it
The stuff you wrote, I believe
but you first rewrote it in a different form. that's what I'm talking about.
sullen crystal
but you first rewrote it in a different form. that's what I'm talking about.
there is used one, but it is not necessary.
you can simply multiply it out like on the 2nd step
you would get $\frac{1}{36}x^4 + \frac{1}{16} + \frac{1}{16} + \frac{9}{64x^4}$
i'll write it in latex but it's a matter of 30sec expanding
stiff viperBOT
adonhs
sullen crystal
just multiplying out
then you can do the same trick as yesterday
also notice 9 and 64 can be written as squares
and the x too
and 36 too
pliant moth
how is it not $$\frac{1}{36}x^4+\frac{1}{8}+\frac{9}{64x^4}$$
wait that's the same thing lol
stiff viperBOT
jarker
sullen crystal
and 1/4 * (9/16)x^-4 = (9/64)x^-4
like 4 * 16 = 16 + 16 = 32 and nother 16 + 16 = 32 so we get 64
pliant moth
$$\left(\frac{1}{6}x^2+\frac{3}{8x^2}\right)^2 = \frac{1}{36}x^4+\frac{1}{8}+\frac{9}{64x^4}$$
stiff viperBOT
jarker
sullen crystal
i also assumed that those tasks are made to be solvable this way and that you dont need to use "complete the square" technique
1/8 = 2/16
pliant moth
ah
lol
It's still not correct. here I'll give you the original trinomal
maybe I grouped it wrong.
$$\frac{1}{9}x^4+\frac{1}{2}+\frac{9}{16}x^{-4}$$
stiff viperBOT
jarker
pliant moth
I just split the 1/2 into 1/4 + 1/4
pliant moth
this is the original trinomal
sullen crystal
ok
pliant moth
oh I fd up big time huh
pliant moth
**jarker**
god I'm an idiot lmaooo
sullen crystal
$$\bigg(\frac{1}{3}x^2\bigg)^2+2\frac{1}{4}+\bigg(\frac{3}{4}x^{-2}\bigg)^2$$
stiff viperBOT
adonhs
pliant moth
what a waste of time
sullen crystal
what a waste of time
stop this fucking negative self talk
you are not an idiot
shit happens
pliant moth
**jarker**
I gave the complete wrong equation. aren't you disappointed a little bit lmao
pliant moth
**adonhs**
so you do this when you are given a 4th power?
sullen crystal
so you do this when you are given a 4th power?
generally use the approach from yesterday
to write it in terms of $a^2+2ab+b^2$
stiff viperBOT
adonhs
pliant moth
ah
sullen crystal
you can also check 2ab
$2\cdot \frac{1}{3}x^2\cdot \frac{3}{2}x^{-2} = 2\cdot \frac{1}{2} \neq \frac{1}{2}$
stiff viperBOT
adonhs
sullen crystal
ok you already said that it's wrong but to see my point of checking if 2ab adds up
because we wrote it like 2 * 1/4
pliant moth
**adonhs**
so then it would always be (a+b)^2?
omg that is so useful. thank you so much
💀
sullen crystal
it's over for you
pliant moth
so it's $\left(\frac{1}{3}x^2+\frac{3}{4}x^{-2}\right)^2$
stiff viperBOT
jarker
sullen crystal
**adonhs**
yea i did here a mistake mb
it should have been 3/4
it's correct congrats