Examples (NCERT) : Part 6 - Binomial Theorem Video Lecture | Mathematics for Airmen Group X - Airforce X Y / Indian Navy SSR

hello friends this video on my numbing
theorem part 6 is brought to you by exam
fear calm no more fear from exam before
watching this video you should have
watched my name in serum part 1 - Part 5
take one of my novel example little easy
where we have to bind X plus 4 number 5
when we know this formula that we have a
plus B to the power and this guy is
nothing but summation off the start
karlsville to 0 to n will say NCR we can
either say a to the power r b to the
power n minus r or we can also say the
same thing as both are true actually
so we can say NC r a to the power n
minus r we delivered are both are same
actually you see a plus B to the power n
or be pissed it will burn both are same
actually so you say NCR and you first
take a to the power R will be 2 power n
minus R you keep decreasing this valuing
things well or you first see a 2 power n
minus 1 B to the power can take any of
this both of these will give you the
same result it didn't show you awesome
so here let's take this one this one
with this so here X plus 4 the v snare n
is equal to 5 this guy becomes 5 cr8 the
power 5 minus r needs about our
summation r is equal to 0 so let's do
this let's add this from our rizzuto
pipe let's put R is equal to 0 will
become 5 0 8 over 5 bit over to 0 so
that's 1 5 C 1 a to the power 4 B to the
power
sorry X plus four so here instead of a
we have X and here is your B we have for
this is the pound and so we'll say five
C 0 X to the power 5 here we'll say X to
the power 4 and we should have E is a 4
will about 1 plus y is a 5 C to X to the
power 3 and 4 to the power 2 so you're
increasing the value of for us a 5 C 3 H
to the power whole and for 2 bar 1 plus
this is 5 C naught 5 C 1 5 6 2 5 see 3
and this becomes 5 sorry this is true
yet increase the value of force come
free and then this becomes 5 C over X to
the power y degrees a value up as become
1 increase the value of 4 put power 4
plus 5 C 5 X to the power 0 is 1 to 1
and proof of God this is the formula so
what if done we have taken five that is
going to Phi R is equal to 0 1 2 3 4 5
you increase and we replace the value so
here R is going to 0 PI minus 0 PI o PI
minus 1 or Phi minus 3 PI minus 3 this
is 2 pi minus 4 is 1 and 5 minus 5 0
exposition similarly if I put the power
R go to bar 0 1 / 2 power 1 foot bar -
for the battery for the Pocoyo why
that's wrong we invert this so we can
solve this v c0 is PI 1 this is actually
where 5 5 C 1 is 5 5 into 4 0 5 into 4
x4 + 5 C 2 is equal to 10 10 into 4
squared 16 X cube plus 5 C 3
again is equal to 210 10 into 4 4 to the
power 3 is equal to 64 and this becomes
X square plus 5 C 4 is equal to 5 into 4
to the power 4 4 to the power 16 is 16
16 is 256 and this becomes X to the
power 1 plus 5 C 5 begins by the 1 into
4 to the power 5 is equal to 1 0 this is
the answer we have got X bar 5 plus 20 X
4 plus 160 X cube plus 648 square plus 5
into 3 solicits is equal to X 2 1 2 is
only 1 that's 1 0 this is the answer
this is a power X plus 4 but 5 now we
have solved this problem using formula 2
because the formula we have used now
let's try to prove that we can do the
same thing with in formula one also will
try to do so here when we expand our x +
4 to the power 5 we can also write this
as summation R is relative
0 2 5 5 CR so instead of saying X 5
minus R we can say X to the power R and
forgotten by - ah that's what we have
discussed either we can see 8 2 power R
be 2 power n minus R or we can see e to
the power n minus r PT power so here we
have taken X to the power 5 minus R and
porta power so in this series we are
taking X to the power 4 to 1 5 members
are so we will try to prove this so if
you do this will say 5 c 0 X to the
power 0 is equal to 1 and porgy the
power 5 plus 5 C 1 X to the power 1 into
4 T power o + 5 C 2 X square over Q + 5
C 3 X 4 over 4 plus PI C naught over 5
so 5 C 1 X 4 this is 5 C 2 sorry this is
we increase the power of X in degrees a
power 4 become X square X cube this will
become X 4 5 C 4 X to the power 4 into 4
power 1 plus 5 C 5 into X to the power 5
so what we have done we have increased
the power of X this time X to the power
0 X to the power 1 2 3 4 pi decrease the
power of 4 for the power 5 over 4 PI
over 3 for the power to will / 102 power
0 and vice is 0 5 c 1 5 c25 c350 by 7
tell you this formula so now 5 C 0 is 1
and 4 through 5 to a 5 is 1 0 semilla 5
C 1 is 5 and food T power 4 is 256
and missus into X plus 5 C 2 is nothing
but 10 into 4 into 3 is equal to 4 into
4 cube is go to 64 X square plus 5 C 3
is also 10 into 4 squares go to 16 xq +
5 0 is 5 into 4 X 4 + 5 suffice for the
one influencer so what you get is I like
these number first because we have to
prove this goodness so this is go to X 5
list em first plus 5 into 4 xx x 4 plus
16 into 10 160 xq + 64 into 10 640 x
squared plus 2t 6 into 5 1 - 8 0 x + 1 0
so you see both are same exactly same so
that means we can use either the formula
we can either first see we can see a
power our B into B to the power n minus
R or we can say a to the power n minus 1
will be the power so both the form X
correct thank you
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