Hello everyone, as we've seen in our previous session .algebra is used quite frequently
in our day-to-day lives may be sometimes we won't realise it.
Let us discuss some situations & learn some interesting concepts in algebra.
Suppose a SCHOOL decides to go on a picnic.
Teacher has given 2 choices to students.
--- a water park and a football match.
Some students chose waterpark and some decided for football match.
Students going to visit waterpark needs to pay amount 120 as fee, whereas, the students
who will be going for football match will have to pay 150 as fee.
Now the teacher wanted to know the total amount collected for all the students GOING FOR WATERPARK.
For 1 student fees is 120, so for 2 students amount will be 120 * 2 i.e. 240.for 3 it will
be 120 * 3 i.e. 360.so on.
But as of now he doesnt know, the number of students going for waterpark.
.. Therefore he took the number of students as
SO, the amount will be 120x right?
Similarly if y numbers of students are going for football match then the total fees FOR
IT will be 150y.
Therefore the total amount for both the places can be calculated as
120x +150y If we closely analyse here 120 and 150 are
the fees which is a fixed amount, whereas x and y are the number of students which may
vary.
So, suppose there are 40 students in total, then x + y = 40
Does this look familiar?
---- YES!!!!
In our previous session, we've studied about algebraic expression, equations, constants
and variables.
So if 30 students are going for waterpark and 10 are going for football match then total
amount will be, 120x +150y
120(30) + 150(10) = 3600+1500 = 5100 so on Here, 120 & 150 are called constants, x and
y are called variables & when they combined with the fundamental operations forms algebraic
expression.
Let us proceed further to learn few more things related to algebraic expressions.
Term Factors
Coefficients Like terms
Unlike terms Degree
Classification
Here the formula to obtain the fees for students going for waterpark i.e.120x is called as
a term.
Similarly 150y is another term.
Let me tell you one interesting fact about a term, when you have only one term, its also
an expression.(one note will appear on the screen)
Now suppose after visiting waterpark, the same number of students are again going to
visit the museum with 200 as an entry fee, then what will be the total amount??
It will be 200x.
Right?
And here 200x is again a term.
Now suppose school HAS already paid 500bucks for snacks for the students visiting the museum,
then the total expenditure will be, 200x + 500
So, here can we call 500 also as a term??
Yes, it is a term In fact here variables x and y are also called
terms.
So let's define a term now, A Term is either a single number or a variable, or numbers
and variables multiplied together in an expression So, finally, the amount spent on the whole
trip, i.e., waterpark, football match and the museum is
120x +150y+200x + 500 Here we can see that the terms are added together
to form an expression.
(Will highlight the things described) Friends we now know that a term is basically
multiplication of numbers and variables and these numbers and variables are individually
called as factors.
So here fees 120 and no of students x are the 2 factors of the term 120x..
Similarly 150 & y are called as the factors OF 150Y ..so on
Note that there can be many factors to a number, for eg 2*60*x is again =120x so 2,60 & x are
also factors of 120x and so on.
( will show factors for all at once) Now we can also see that the factors are either
numbers or variables.friends the numerical factors are called as coefficients and we
read it as 120 is a coefficient of'x', 150 is a coefficient of 'y' and so on.
I hope you've understood everything so far.
Now if you remember, the same number of students who went to the waterpark visited the museum
too & so we took the same variable x to form both the terms and such terms are called as
like terms.
120x +150y+200x So, 120x & 200x are called like terms.
And mathematically like terms are those terms that have same variables and their powers.
On the other hand terms which do not have same variables with their powers are unlike
terms.
Here, 120x & 150y , 150y & 200x are unlike terms
As I've said something about power in the definition of like terms.
What is power??
Power of a number says that how many times a variable or a number is multiplied.
For eg.25 is obtained by multiplying 5 twice so here 2 is the power of 5.
In an expression the highest power of a variable defines the degree of that expression.
Here the degree is 1.
Now look at this expression x^2+x^3+4xy-y^2+8x^2 y
Can u tell the degree of this expression..
It is 3 bcus the highest power of x is 3.
Now if I remove x cube then now can you say the degree?
Are you going to say that the degree is 2?
x^2+4xy-y^2+8x^2 y So let me tell you if you thinking that the
degree is 2 then you are wrong.
Here the degree is still 3.
Because when we have 2 variables in a term , we should add the power of both.
Now the last thing that we are going to understand is the classification of expressions....
Friends algebraic expressions are classified based on its number of terms.
As we studiedjust an expression can be of a single term.it can have 2 terms, 3 terms
or simply it can be of more than 3 terms.
So friends when we have one term ,the expression is called monomial.
A MONOMIAL IS ANOTHER NAME OF A TERM When we have 2 terms we call it as binomial
expression having 3 terms called trinomial.
And expression more than 3 terms is simply called polynomials
An expression containing two terms is called ab inomial.
(Bio means two) An expression containing three terms is called
a trinomial.
(Tri means 3) An expression containing more than3 terms
is called a polynomial.
(Poly means many) Let's check how much we've understood by attempting
the following questions Factors of the term 6xy is__
6, x, y 2,3,x,y
6, xy All above
Reason: 6xy = 6xy
NOTE: A term may have many factors.
Like term to the term 27x3y2 _________ 27 x2y2
-3 x3y2 9 x2y2
7 xy 27x3y2, -3x3y2
Both have same variables & their powers.
Degree of the expression: 9x3 + 7x2y2 + 8xy 2
3 4
6 Highest power of the term 7x2y2 is 4.
State the type of expression?
Now, having understood algebraic expression well & different notions involved now I am
curious to know, what if we can add two algebraic expressions together or if we can subtract
& multiply them just like we do with numbers because in algebraic expression along with
the numbers, variables are also used.
So how to do basic operations (+, -, ,/) with algebraic expressions?
We are going to learn these things in our upcoming sessions.
So friends, I am sure you have found this session easy, useful and understood the various
concepts that we discussed today.
But still in case you have any query, do not hesitate to ask us by posting your valuable
comments in the below comment box.
Till we meet in the next session, keep watching, keep learning