Examples: Addition and Subtraction Numericals Video Lecture | Mathematics for Grade 6

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addition and subtraction of algebraic
expression we will look at some of the
questions question number one what
should be added to x squared plus XY
plus y squared to obtain two x squared
plus three X Y so in this question we
have to find out let's say this is one
expression which is given so what is
that expression which should be added to
this expression such that the result is
two x square plus three X Y so you
basically need to find out this question
mark that is this expression so in order
to find out this expression what you
would do you just move this entire
algebraic expression towards this side
and we know that whenever we transpose
the value whether we transpose a
constant or a variable from one side to
another the sign changes that means if
we are trying to find out the value of
this question mark then this is going to
be equal to two x square plus three X Y
which is this term minus X square plus
XY plus 5 square that's because on the
left hand side the side of positive sign
the moment we shifted to the right hand
side this would carry a negative sign so
therefore we basically need to find out
the difference between these two
expressions so let's rearrange them to X
square plus 3 X 5 minus X square minus
XY minus y square now let's collect the
light terms together that is 2 X square
minus X square together plus 3xy minus
XY this together minus y square so 2 X
square minus 1 X's squared so 2 minus 1
is 1 so this would be 1 X square plus
3xy minus 1 X Y so 3 minus 1 is 2 so
would be 2xy minus y square X square
plus 2xy minus y square would be the
answer question number two what should
be taken away from 3 X square minus 4y
square plus 5 XY plus 20 to obtain minus
X square minus y square plus 6xy plus 20
so that means you are given an
expression 3x square minus 4y square
plus 5xy
plus 20 so you are asked that what is
that number which should be subtracted
from this expression so this time you
are subtracting some number from this
expression so that you get something
like this minus X square minus y square
plus 6xy plus 20 so we have to find out
the value of this question mark so in
this case let us say that if we move
this question mark to this side and if
we move this and diatom to the side or
if we keep the question mark here and if
we move this entire term to this side
then what would happen so basically if
you keep the question mark here but the
question mark will have a negative sign
and if you shift this entire term so
this entire term has a plus sign when it
is on the left hand side but the moment
we will shift it to the right hand side
what would happen the plus sign would
get changed to the minus sign so this
would be minus 3x squared minus 4y
squared plus 5x y plus 20 but this would
be minus question mark but we need to
find out the value of the question mark
so that means you need to shift this -
angle to this side so the whole ending
shift to this minus side here what
happens that desired the the sign of the
result also changes correct so what
happens so let us assume if we as you
that this entire value is a and this
entire value is B let us assume that so
that means we had a minus B on the right
but the moment is shipped this negative
sign this side so you get minus a minus
B which is equal to minus a plus B so
basically a minus B becomes B minus a so
in this case that is what we need to
find out so we basically need to find
out B minus a so B is three X square
minus four Y squared plus five x y plus
20 this entire thing minus minus X
square minus y square plus six Y plus 20
so let us rearrange the terms by opening
the brackets so you get three X square
minus four Y squared plus 5x y plus 20
plus X square plus y square minus six X
Y minus 20 so let us collect all the x
squared terms together three X square
plus X square minus 4 y squared plus y
squared again y plus 5xy minus 6x y plus
20 minus 20 so three X square plus one x
squared would be 4 X square minus 4 y
square plus y square would be minus 3y
squared because minus four plus one is
minus three it came plus 5xy minus six X
Y would be minus One X 1 because plus
five minus six is equal to minus one
plus 20 minus 20 would be zero so
therefore we see that 4 X square minus 3
by square minus X Y this would be the
result Pesce number three from the sum
of three X minus y plus eleven and minus
y minus eleven subtract 3x minus y minus
eleven so first of all we need to find
out the sum of these two expressions so
3x minus y plus eleven this is one
expression plus minus y minus
so how do we find the sum we rearrange
the terms first of all so this is how we
rearranged let's bring the same book
this the light terms together so 3x
minus y minus y plus 11 minus 11 so this
would be equal to 3x minus y minus y
would be minus 2y plus 11 minus 11
rooting 0 so 3x minus 2y would be the
sum now what we have to do from this sum
we need to subtract 3x minus y minus 11
so this was the first part so in the
second part what we do from the Sun that
we get which is 3x minus 2y we subtract
3x minus y minus 11 so here also let's
rearrange the terms so we get 3x minus
2y minus 3x plus y plus 11 so therefore
here again place the like terms together
3x minus 3x minus 2y plus 5 plus 11 so 3
plus 3 X minus 3 X would be equal to 0
minus 2 y plus y that would be minus y
plus 11 so 11 minus y would be the final
answer
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