Examples Finding Value, Number patterns Video Lecture - (Maths) Class 7

hello friends this video on algebraic
expressions part 13 is brought to you by
exam feel calm no more fear from exam so
let us quickly look at some of the
questions where we will see some
applications of expressions and also
finding out the values of expressions
question number one if Z is equal to ten
find the value of Z cubed minus 3 into
said minus 10 so same cube is said in to
second to Z minus 3 into Z minus 10 so
let's replace Z with 10 so this would be
10 into 10 into 10 minus 3 into 10 minus
10 so what would be 10 minus 10 0 and 0
into 3 would be 0 and what would be 10
into 10 into 10 that would be thousand
so thousand would be the answer question
number 2 what should be the value of a
if the value of 2 X square plus X minus
a is equal to 5 when X is equal to 0 so
that means if you put X is equal to 0 so
what will happen 2 into 0 plus 0 minus a
is equal to fine right so 2 into 0 would
be 0 so 0 plus 0 minus a is equal to 5
so 0 plus 0 would be 0 so minus a is
equal to 5 therefore a is equal to minus
5 question number 3 simplify the
expression and find its value when a is
equal to B for easy and find its value
when a is equal to 5 and B is equal to
minus 3
so look at this expression it is 2 into
a square plus a B plus 3 minus a B so in
order to simplify this let us first open
it out from the brackets so 2 into a
Square will be 2 a square plus 2 into a
B would be 2 a B plus 3
a B so let's collect then like terms
together so 2 a square plus 2 a B minus
a B because both of these are like terms
both of them have the same algebraic
factor which is a V plus 3 so 2 a B
minus a B will be equal to a B because 2
minus 1 is 1 so plus a B plus 3 so now
this would mean 2 into a into a plus a
into B plus 3 now let's put the value of
a the value of a is given as 5 so 2 into
5 into 5 plus 5 into B is minus 3 so 5
into minus 3 plus 3 so 2 5 10 10 times a
55 3 is a 15 so this is minus 15 plus 3
so 50 plus 3 would be 50 3 minus 15 so
53 minus 15 would be 38
so 38 would be the value of this
expression question number 4 use the
given algebraic expression to complete
the table of in upper patterns so here
if you look at this table it shows a
number pattern so you see you have an
expression which is 2 n minus 1 so if
this is the expression now as the value
of n changes you get different terms for
example when n is equal to 1 the first
term is 1 where n is equal to 2 the
second term is 3 now when you look at
this pattern it follows a specific
pattern that is 1 you leave - you come 3
4 & 5 6 7 8 9 and so on so it follows a
specific pattern so we have to find out
these blank fill these blank spaces
based on this pattern so how will we
know the pattern looking at this
expression okay so now looking at this
expression let us first try to fill this
blank so in this blank we have to find
out the 5th
so in order to find out the fifth term
we will make use of this expression so
what we will do we will put M is equal
to 5 in this expression n square plus 1
so what do we get n square plus 1 would
be enter into n plus 1 which is equal to
5 into 5 plus 1 that is 25 plus 1 which
is 26
therefore this blank would be 26 now
that is look at this term it is the 10th
term for this that means you will put n
is equal to 10 in the expression n
square plus 1 so this would be n into n
plus 1 which is 10 into 10 plus 1 so 10
into 10 is hundred plus 1 which is equal
to 101 therefore the value here would be
hundred 1 now let us look at the third
plan which is the hundred digit undreds
number for this particular expression so
in this case we will put n is equal to
hundred in the expression 2 n minus 1 so
this would be 2 into n minus 1 which is
2 into hundred minus 1 so 200 minus 1
that is equal to 199 so here this would
be 199 and how did you realize why did
we put n is equal to hundred to find the
heart rate down because when you look at
this pattern you see that to find the
first term you put n is equal to 1 so if
you put n is equal to 1 the value of
this expression is 1 if you put n is
equal to 2 the value of this expression
is 3 so we get an idea that to find the
first term we put n is equal to 1 to
find the second term we put n is equal
to 2 to find the third term we put n is
equal to 3 therefore to find the
hundredth term we will put n is equal to
hundred so with that logic we have put
the value of n as hundred so we make use
of this logic and that is how we you
know we build number patterns so I hope
this lesson on algebraic expressions
would have helped you
and I expect you to practice more and
more question so that you can build your
confidence and you can build your
concepts better so see you all in the
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