L8: Questions - Factorization, Mathematics, CBSE Class 8 Video Lecture

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question number 5 factorize this
expression X to the power 4 minus X
minus Z to the power 4 looking at this
can you think of any identity into which
you can kind of put it yet you can you
can take help of the identity a square
minus B square is equal to a plus B into
a minus B because both of these terms
are perfect square so X to the power 4
can be written as X square to the power
2 similarly X minus Z to the power 4 can
be written as X minus Z whole square to
the power 2 so this is basically end up
on a square minus B Square that X is
squared behaves like a and X minus red
whole squared his light-bee
so this becomes a plus B that is x
squared plus X minus red whole square so
this is a plus B into a minus B that is
X square minus X minus Z whole square
now next you one thing let's break down
this X minus red whole square so X minus
bed whole Square will be equal to a
squared minus 2 a B plus B Square where
a is equal to X and B is dead similarly
in this case also we will do the same so
this becomes x squared minus 2x Z plus
red square now do you understand why I
had retains the bracket set because here
we have a negative sign if you try to
remove the bracket and eat the scene
inside it will create a contusion so it
is better that you break it down but you
still eat the bracket impact now here is
X square plus X square this becomes 2x
squared minus 2x red plus red square and
what happens here is here it becomes X
square minus X 2 square plus 2x
red plus plus into minus and minus Z
square so X square minus X 2 square
would be zero so this becomes equal to 2
X square plus Z square minus 2x bed into
2x minus Z square if you look at this
term pew has said in common
so this can further be written somewhat
like this take out red in common so this
becomes 2x minus Z so this is the final
factored form and hence the final answer
for this expression question number six
the first expression is Q square minus
10 Q plus 21 so this is that type of an
expression where even though you have
one variables you have three terms but
the two terms are not perfect with only
one term is the perfect square the other
one is not in this case Q square is
perfect square the 21 is not so that
means this will fall under the category
of the special identity that is X plus a
into X plus B is equal to X square plus
a plus B into X plus a into B so let's
see if we can guide to this equation in
this format so X 2 square is Q square Y
minus 10 into Q so can we write minus 10
as sum of two numbers
well minus 10 can be written as minus 3
plus -5 and so minus 3 plus minus 10 is
equal to minus 10 should this into Q so
Q square plus 8 plus B into Q plus a
into B that is minus 7 in to minus 3 so
you see we have very perfectly written
it in this format so therefore this can
be written as how can we write it this
is equal to X plus
into X plus B X is Q here what is a a is
-7 so Q plus minus 7 into Q plus -3 so
this can be written as q minus 7 into Q
minus 3 so I think here you have to read
this this step is where you need to be
smart enough to write it in this form so
that you are able to satisfy this
expression at the same time you are able
to write it into this expression form
next one is a to the power 4 minus 2 a
square d square plus B to the power 4 so
here also if you look at a to the power
4 this is a perfect square it can be
written as a square whole square if you
look at B to the power 4 this is also a
perfect square so you can write it as B
square whole square now if you look at
the middle term this can be written as 2
into a into B so here is well behaved
like a and B squared is like B that is a
square minus 2 a B plus B Square so this
is a minus B whole square so that is a
square minus B Square Holtzman so he had
a square is behaving like a be fed is be
gaining might be now a square minus B
Square this can be written as a plus B
into a minus B this entire things whole
square so this can be written as a plus
B whole square into a minus B whole
square so this is the factored form so
in this fashion we saw that we are able
to factorize different types of
algebraic expressions using these four
techniques thank you please visit
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