leaving just one A
ba - a
a(b-1)
(2/3)^x times (16/81 - 1)
a moves to the outside
no break until i understand
you can imagine factoring as pulling the thing that's in everything outside of each of them
then writing a parenthetical with the empty husks of whats left after their commonalities are extracted
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SIMPLER PROBLEM:
why do i understand this intuitively
and then be completely unable to comprehend the other one
how can i set this up to be more comparable with the problem im struggling with
its the order of operations thats fucking with me
i feel like i should HAVE to take care of this
before i can take care of this
why is that not the case
too-specific drilling. look at (2/3)^x as a single term a
when you suspect factoring is necessary, order of operations is out the window specifically because factoring is to pull something out of the entire expression to effectively change the order of operations
i mean if u squint a little it stops feeling as factoring at all cuz its just 4x-x = 3x except the 4 is 16/81
then from here order of operations is broken?
wait
theres nothing broken its just that that is clearly equal to (b-1)a
just like 4x - x = 3x
stop typing
BA - A = A (B - 1)
or
B*A - A = (B - 1)*A