Examples: Factorisation using Identities(Part 1) Video Lecture | Mathematics for Super TET

he'll open this video on factorization
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no more to your exam question number 4
factorial again we have two expressions
the first let's look at the first one
25 a square minus 4 d square plus 28 BC
minus 4 2 9 v square over so now if you
look at this expression you have four
terms out of which you have three
different variables like ABC and that
two out of the four terms you have three
terms which are quadratic and a square B
Square C square now quite difficult to
handle it seems right okay let's do ante
next first handle three of these try to
fault that make it simpler and then take
the fourth one along let's take a couple
of seconds to analyze each term so if
you look at the first term it is a
perfect square so 25 a square can be
written as 5 a whole square if you look
at the second term this is also a
perfect square because for these quaint
and originals 2 D whole square if you
look at the last term this one also is
the perfect square because you can LTL c
7c couple squares I want you to see what
will be tones are open square now the
question is which three terms should be
first considered because you know we can
apply we can be use of identities like a
plus B whole square or a minus b whole
square we need to treat them because we
would need something in the form of a
square plus 2 a B plus d square right so
what we have to use on which terms we
need to select that will be decided by
system so when you look at this term it
involves two variables B and C so that
really tells us that we can only
contribute distance B Square and this
term C square so let's see if this part
fits into our formula or not so what we
will do let's keep 25 a square aside for
now and let's take everything else
inside a bracket for example we take
this 4 d squared - 28 BC + 49
C square insider practice now while the
signs revert because we are taken - in
common so entities minors in common that
means we are basically taking out the
common factor of minus 1 from each one
of these ok so now let's just try to
solve all that we have inside the
bracket so 4 d square can be written as
2 B whole square
49 3 square can be recognized 70 volts
leg so the midget terms must be written
as 2 into a into B - just check if this
value is equal to this or not so this
would be 2 to the 4 4 7 the 28 - 28 BP
perfect so this this fits into it
ok I just missed the minus sign here so
this would be 25 a square - this is a
square minus 2 a B plus B square that is
a minus b whole square so you have 25 a
square minus 2 B minus 70 whole square
now and we mentioned just now 25 a
square can be written as 5 a whole
square minus 2 B minus 70 whole square
now that this expression remember any
identity that you have done so far yes
it does it is in the form of a square
minus B Square there file is in the
present a and 2b minus 70 together
represents B so a square minus B Square
will be equal to a plus B into a minus B
so a plus B into a minus B so this is a
minus B so this would be our answer so
then you deal with this kind of
expression so you need to be little
extra cautious that you because many a
tiny like watching these type of
expressions people often painten's we
blow the minus sign and therefore they
commit a lot of missing so please make
sure that it will not oh my
sign and if you taking the - and comment
to the friends inside would all get
reversed still getting displeased or
think you'll see a plus B this is what
they're put three one no state like a
plus B into a minus D so now when you
open the inside plus first bracket this
is what you will get
so these are small for things which you
should keep in mind okay now let's move
on to the next expression L n plus L
plus M plus one so here if you look at
the first five first killzone you see n
is a common factor so let's take n out
so this becomes n into n plus one plus n
plus one now let's compare this term and
this term what you have in common n plus
one is common if you take out n plus one
in the first time you're left with L in
the second term you next with one
because n plus 1 into 1 is n plus one so
what is this this is the factored form
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