Addition of Algebraic Expressions - Algebraic Expressions, Mathematics, CBSE Class 8 Video Lecture

hello friends this video on algebraic
expressions part 7 is brought to you by
exam feel calm no more your cram exam so
now that we got a fair idea about
analytic expression now the next
question that might bother you in how do
we perform different operations and
algebraic expressions for example if you
are given two expression 5x + 3 y
squared now if I ask you to add these
two so how do you add them now sounds
difficult is complicated as well so if I
give you any two expressions now these
expression could be erroneous binomial
or polynomial whatever so how when you
perform addition or subtraction of
algebraic expressions now the next
question that might strike your mind is
can we do addition and subtraction on
expressions as simply as you do them on
numbers like 5 plus 3 is very easy to
add but can we add 5x plus 3y squared
that easily or can we add or subtract
any two expressions or there are some
conditions that only certain types of
expressions can be added together and
certain timings can not be added
together so let us learn in detail about
the addition and subtraction of
algebraic expressions let us first talk
about addition of algebraic expressions
now there are certain steps that we
follow to add algebraic expressions
first of all we arrange the tone now why
do we rearrange terms because we want to
collect the light terms together so let
me take examples so first we will take a
very simple example let's say you are
given two terms 5x + 8 X and you have to
add these two now here this is simple
because you just kept it on which you
need to add and the body terms are like
terms right because both of them have
seen and should risk factor which is X
so they are already like them so you
really do not need to rearrange term
fine now add the like terms how do we
add like terms numerical coefficient of
the result is equal to sum of numerical
coefficients of the terms so in this
case what is the numerical coefficient
or
the Sun so the numerical coefficient of
this term will file numerical
coefficient of this term is 8 so you add
the numerical coefficient that is 5 plus
8 you add the numerical coefficient and
leave the algebra coefficient as it is
so 8 plus 5 is 13 so the sum of pilots
and in a Texas 13 8 so that is how we
add like terms now let me take another
example and we will try to add these
following the same steps let's say that
you have to add 3 y squared with 1 by 2
y squared so in this case our team to
term like terms get they are light
because both of them has been algebraic
factor that is my friend so again we can
follow the same technique as the numeric
coefficient of the two terms so 3 times
1 by 2 by square 3 plus 1 by 2 is 7 by 2
so the result would be 7 by 2 y square
so we will take one more example so
let's say in the third example we see
you have to add Y square plus 1 this is
one algebraic expression and the other
algebraic expression is X plus 1 so you
have to add these two editing
expressions now till now in example 1
and 2 each and every expression was a
monomial in this case each of them is a
binomial so we are going to be adding
two binomials so this means Y squared
plus 1 plus X plus 1 so in that case all
the terms are not like them to the need
of rearrangement start next we need to
rearrange them so let us try to
rearrange all the terms which as a risk
factor Y square together so how many
terms do you have with algebraic factor
Y square only one term that is y square
now let us collect all the terms
together with algebraic factored in for
that also we have just one term it is 8
now let's collect all the terms with no
energy risk factor that is basically two
constant terms together
how many constant terms you have two it
is one and one so let us put these two
together now we can all these I
the light term we can in fact we can
only ask the light them so what will
happen one plus one is two
so Y squared 2x plus 2 is the sum of
these two algebraic expressions now you
might ask with how can we add y squared
of X we cannot add them so we can only
add the light tones in an expression we
cannot add the unlike terms together so
the result of these sum of these two and
the big expressions or the result of the
sum of these two binomials would be
another trinomial okay so if this
concept is clear let's take one more
complex example let's say you are given
one expression is y squared plus 1 and
the other expression is py squared plus
y plus 2 and you have to add these two
so how will you I tell the Y square is 1
plus 3y squared plus y plus 2 so let us
start arranging the like terms so y
square + 3 y squared is an item because
both of them have seen as if we factor
that is y square so he puts 10 together
now how many terms do you have these are
degree factor while only one term so we
put it together how about the constant
terms there are two constant terms 1 & 2
so we put them together and a y squared
+ 3 y square so what would be the sum
for y squared the numerical coefficient
is 1 so 1 plus 3 that is 4 by squared so
this becomes 4 y squared + y + 3 so 4 y
squared + y + 3 would be the sum of
these two and if it expressions so the
concept is pretty simple it is just that
you need to arrange the like terms
together because you can only add the
like terms together okay so now let us
do some exercise on adding and civic
education because in the previous slide
we took mostly simple example so let's
say that you are given these three
algebraic expressions and you have to
add them TMI with 8pz 3p bed -
in red minus P now in the previous slide
we took separate monomials and binomials
so it was pretty simple to collect the
terms together but when you have bigger
artistic expressions then the work of
the inch in two terms sometimes becomes
tedious and complex so to avoid that
what we do is there is a better way of
adding the expression so let's look at
the space so you write down the first
expression 8 minus P 8 P minus 8 D Z so
we rotate perfect now when it comes when
the term for the second expression comes
instead of writing it besides with
expressions right the second expression
below the first expression such that all
the like terms are written just below
each other that means in the second
expression you have three P Z so creepy
red is L is like term with 8 TZ tonight
right ptuh just below 8 event so please
use it has a plus sign before next okay
and what is the other term here the
other term is there but in the first
expression you do not have any toe with
dead so we will not write dead below T
because red and T they are not like
terms so let us write Z separately in a
different corner with a new color all
together now let us move on to the third
expression which is red minus T so rate
or your thing you should put dead below
each slight turn so red and dead they
are like terms let's put dead below yes
but this time dragged as a plus sign and
the next term is minus P so red will
reach put minus T again with the light
term so minus P will be like big plus P
so we put minus P here next
so in this way we arranged these three
algebraic expressions now what we do so
for the first derivative patient we have
two terms in the place of the third term
it has nothing so we can write it as 0
for the second expression the first term
we have nothing tonight right LP dome
similarly first in case of the card and
every expression the middle term is
nothing
for this video perfect now let us add
these three so with this arrangement
there is no chance of making a mistake
because you know you can see that the
light sound has been put together or not
so now let's add D so now when you is t
minus T is what plus t minus T would be
0 similarly minus 8 plus 3 TZ
so obviously the a degree part will
remain the same but they are like terms
just focus on the numeric part it is
minus 8 plus 3 which makes it - fine
again here - 8 + red is 0 so therefore
the sum of these three algebraic
expressions would be minus 5 TZ so this
would be the sum now let us try one more
example so that you know we get familiar
with this technique so here again we
have three different algebraic
expressions and each and every
expression has three terms let's start
with the first one first one is a plus B
minus 3 so he write this as this next
one is B minus a plus 3 so where can we
write B D is actually plus B so we write
it below B minus 8 we will write it
below 8 and / 3 label right is below
minus 3 what about the third expression
it is a minus B plus 3 so kad will write
below a minus B again in the right is
below plus B and slash screen we will
definitely write below the field so now
we have all the YZ together on the B's
together and all the constant terms
together let's add them so in this is e
plus a.22
is together will be 2 8 minus 8 so
overall it will become a similarly get B
plus B that is 1 B plus 1 we will make
it to be minus 1 B that is again 1 that
is B here 3 plus 3 would be 6 minus 3
that is plus 3 so again a plus B so when
we put on these sums so if again follows
the same concept of board man that is
whenever you have to plug so you perform
the addition first and then you
subtraction for example here D plus D we
perform the addition purse which is to
be minus D that makes it one so in this
fashion in this case the sum of the
three ensure break expressions would be
a plus B plus three
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