Examples: Division of Algebraic Expressions Video Lecture | Mathematics for Super TET

hello friend this video on factorization
part 10 is brought to you by example
calm
no more fear calm exam so now based on
the decision of a vivid expression let's
try out a few questions question number
one depend 34 X cubed Y cubed x cube
divided by 2 P 1 XY squared X cube so
here what we will do we will write them
in the form of factors so 34 x SQ y cube
red cube divided by 51 XY squared ed Q
so how do we write this if you prime
factorize 34 this can be written as 2
into 17 into X into X into X into y into
y into y into Z into Z into Z divided by
how can we write 51 51 can be written as
3 into 17 into a into y into y into Z
into Ted into there so here you see 17
entirety will get canceled X X will get
cancelled YY the cancel YY gendell
cancel dead-dead will cancel red red
will cancel red red will cancel so what
I will f2 it in the numerator we are
left with 2 into X into X into y and in
the denominator we are left with 3 so
basically we are left with 2 by 3 X
square Y is the result let's try out the
second one which is PQ q to the power 6
minus 3 to the power 6 cube cube divided
by 3 to the power 3 Q to the power 3 so
as I have mentioned available you have a
binomial divided by a monomial you can
actually mean that TQ q to the power 6
by P to the power 3 q to the power 3
minus P to the power 6 Q to the power 3
divided by P to the power 3 Q to the
power 3 so this is get e to 1 P 2
Chancellor so what is Q to the power
shake that means you have q6 x / q 3
times similarity in the second term Q to
the power 3 and Q to the power K will
cancel out and this time you have six
teams on the top and three T's in the
denominator so t qs will cancel out with
CQ three P's will cancel out with three
teams so what are you left me Q to the
power 3 minus P to the power C question
number two secure again you have
polynomial divided by a polynomial
96 ABC into 3a minus 12 into 5 B minus
13 divided by 144 a minus 4 into B minus
fit so here what we do
let thank the numerator and the
denominator in the form of this factors
so for that lets factorize 96 so 2 into
48 2 into 24 2 into 12 to 6 the 12 to 3
the 6 therefore 96 can be written as 2
into 2 into 2 into 2 into 2 into 3 into
a into B into C now when you look at 3a
minus 12 so if you write 3a in the form
of factors it will be 3 into 8 if you
guys clear in the form of factors it
will be 3 into 4 so 3 is a common factor
let's take out 3 so you will be left
with a minus 4 second hydrofoils be you
can rather than 5 into B and 30 you can
write as 5 into 6 to 5 is a common
factor let's take out 5 so inside you
would have B minus 6
now in a similar way let's write the
denominator so 4 that is going let's
factor is 144 this would be 2 into 72 2
into 36 2 into a 2
- into nine and then 3 into 3 so 144th
and written as 2 into 2 into 2 into 2
into 3 into 3 into a minus 4 into b
minus 6
now let's see what are the terms that
are getting cancelled the 2 2 will
cancel again - to be canceled - to the
cancelling and use 2 will cancel 3 3
will cancel this 3 and this 3 will also
cancel a minus 4 will cancel out with a
minus 4
anything else do you think will get
cancelled out okay
this is not delightful to be artistic so
just by the tape we wrote it so B minus
6 and B minus 6 will cancel so we do not
have anything in the denominator we just
have a 1 and what about the numerator we
have this 2 and then we add this ABC and
then we have to fight so we are left
with 2 into a into D into C into 5 so 2
into 5 is 10 ABC is then one question
number 3 so here again we have a
polynomial to be divided by a polynomial
so 4 by Z into Z square plus 6 Z minus
16 divided by 2y into stage plus 8 here
again when you look at the numerator
this portion of the numerator red square
plus 6 Z minus 16 this can be factorized
so that you can write it in the form of
its factors right that's our purpose
that we want to write the numerator and
the denominator in the form of its
factors so here you have a complete
restoration so we need to factor in it
so that you can write it in terms of its
factors now just focus on this Z square
plus 6 z minus 16 seconds what form
insisted so even though these two are
perfect squares but still it doesn't fit
in the formula of a michael people scale
so that it in that case it has to be a
square
d squared but in this case it is not
Class B spiracles by half v square plus
to it so it doesn't fit in the bottle of
a minus b whole square so let's check if
it fits into this formula x plus a into
X plus B is equal to X square plus a
plus B X plus a into B so you think it
will fit into this formula the sixth can
be written as so how can we write take
the six can be readily written as 8
minus 2 and 16 can be written and eight
into minus two so basically what does
this mean this means that red square
plus minus 2 plus 8 Z plus 8 into minus
2 so we have written it in such a form
such that a is equal to minus 2 and B is
equal to 8 you see in this equation
beginning this false you put L is equal
to minus 2 and B is equal to 8 you would
get this expression right so now as for
that we can write it as X plus a that is
red plus minus 2 which is 8 minus 2 into
X plus B that is X plus 8 so let's write
that in this expression so for Y Z into
instead of this we write Z minus 2 into
Z plus 8 divided by 2 y into Z plus a so
this replicate and regulating 8 we
cancel wiring and viable cancels so 4
divided by 2 so 2 into 2 is 4 so we are
left with 2 Z into Z minus 2 question
number 4
so let us look at this question so in
the numerator we have certain I leave I
cube into 50 Y squared minus 98 divided
by 26 y squared into file provides +7
flesh pattern with the numerator and the
denominator
let's first handled the numerator so 39
can be written as 3 into 13 by cube is y
into y into y now if you look at 50 Y
square minus 98 so 2 is the common
factor so if you take out 2 from this
you are left with 25y squared - 49 now
an interesting thing to observe the
edges 25y squared is a perfect square 49
is also a perfect square
let's see how do we handle with that
right now we are just dealing with the
numerator so this is 3 into 13 into y
into y into y into 2 into this would be
7 y whole square minus 7 square so this
is in the form of a square minus B
Square therefore we can write it as 3
into 13 into y into y 2 divided into 2
into a plus B that is 7y plus 7 into a
minus B that is 7y minus 7 okay okay so
there is a mistake here instead of
reading various where it would be find y
whole square that's how it would be 25
by square right so this would be 5 - y +
7 + 55 y - 7 so you can we have
factorize - the numerators now it's the
turn for the denominator let's work on
the denominator in the denominator it is
26 Y square - 26 can be written as 2
into 13 y square can be written as Y
into y into 5y plus 7 so the same thing
would be here that is 2 into 13
into y into y into y into 5y plus seven
so here again the same thing it would be
2 into 13 into y into 5 into 5 y plus 7
now let's look at the cancellation of
the term coordinated and denominator
turning and turning will get cancelled
YY will get cancelled this Y and Y with
an ingot cancel 2 I 2 will get cancelled
5 I + 7 + 5 y + 7 will get canceled so
what are we left with we are left with 3
1 y + 5 y - 7 so therefore our desired
would be T into y into 5 y - 7
thank you please visit example.com for
free quality education you can learn
with a simple four-step learning process
wearing you can watch video lessons you
can ask your questions you can grab your
notes and you can take a free online
text we have content for class 6 to 12
on physics chemistry mathematics and
biology along with practical videos so
please subscribe to our channel for
daily updates thank you