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3𝑎^7𝑏 − 81𝑎^4𝑏^4

Answer:

3𝑎^7𝑏 − 81𝑎^4𝑏^4

We can write the given question as,

3𝑎^7𝑏 − 81𝑎^4𝑏^4 = 3𝑎^4𝑏(𝑎^3 − 27𝑏^3)

According to the equation,

𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)

So we get,

3𝑎^4𝑏(𝑎^3 − 27𝑏^3)

= 3𝑎^4𝑏(𝑎^3 − (3𝑏)^3)

Using the equation,

= 3𝑎^4𝑏[(𝑎 − 3𝑏)(𝑎^2 + 𝑎(3𝑏) + (3𝑏)^2)]

= 3𝑎^4𝑏(𝑎 − 3𝑏)(𝑎^2 + 3𝑎𝑏 + 9𝑏^2)

"hello guys welcome back to leader
homework i'm revan kumar working as a
tutor that leader
so today we are going to solve one more
very interesting and easiest problem
so let's see how we can do it and how we
can solve it okay so now they have given
here the question it has 3 a power 7 b
minus 81 a power 4 b power 4
right so by this question we cannot do
anything directly
so if you are taking anything common we
can do it right
so if you are taking the common thing as
uh
that is 3 a power a
power 4 b okay if you are taking 3 a po
4 b
as common you will be remaining left
over with here
a q minus 27
uh they are you have taken like a cube
if you are taking a 4 common a cube will
be there and here you will be left over
with
your b cube right so that is only the
thing
so 3 a power 4 b you have to common here
then this will be left over inside it
right so
this will be exactly you can write it in
the format of a
cube minus 3 b whole cube
right so again it is in the format of
what a
cube minus b cube so that is equals to a
minus b
of a square plus a b
plus b square right so that is just
substitute each and everything here so
this is a
and this is b here so after substituting
each you will be getting
a minus three be off a minus three be
off
there a square means a square only place
a
into three b plus 3 b whole square
so that you will be getting the answer
as a minus 3 b
of a square plus 3
a b plus 9 b square so that is our final
answer here
i hope you understand what i've done so
before that there we have took this
common no
so we'll be writing here 3 a power 4 b
so i hope you understand what i've done
here
if you have any doubts please comment
below don't forget to subscribe to this
channel
thank you so much for watching this
please subscribe to this channel for
further updates
thank you
"

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