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Examples: Factors, Coefficients and Types of Expressions Video Lecture - Class 7
FAQs on Examples: Factors, Coefficients and Types of Expressions Video Lecture - Class 7
| 1. What are factors in mathematics? |  |
Factors in mathematics refer to the numbers that can divide a given number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, as these numbers can divide 12 evenly.
| 2. What are coefficients in algebra? | |
In algebra, coefficients are the numerical values that multiply a variable. They are constants that appear before a variable in an algebraic expression. For example, in the expression 5x + 3y, coefficients are 5 and 3.
| 3. What are the different types of expressions in mathematics? | |
There are three main types of expressions in mathematics:
- Numerical expressions: These are expressions that contain only numbers and mathematical operations, such as addition, subtraction, multiplication, and division.
- Algebraic expressions: These are expressions that contain variables, coefficients, and mathematical operations. For example, 2x + 3y is an algebraic expression.
- Literal expressions: These are expressions that contain both numbers and letters. They are often used to represent formulas or equations, such as A = πr^2, where A represents the area of a circle and r represents its radius.
| 4. How do I identify the factors of a given number? | |
To identify the factors of a given number, you need to divide the number by different numbers and check if the division is exact without leaving a remainder. Start by dividing the number by 1, then try dividing it by 2, 3, 4, and so on, until you reach the number itself. The numbers that divide the given number without leaving a remainder are its factors.
| 5. What is the difference between factors and multiples? | |
Factors and multiples are related concepts in mathematics, but they have different meanings. Factors are the numbers that can divide a given number without leaving a remainder, as explained earlier. On the other hand, multiples are the numbers that a given number can be divided into without leaving a remainder. For example, the multiples of 3 are 3, 6, 9, 12, and so on, as these numbers can be divided by 3 without a remainder.
Text Transcript from Video
hello friends this video on algebraic
expressions part 7 is brought to you by
exam for calm no more fear from exam so
based on whatever we have learned so far
on algebraic expression their parts
their types let us have a look at some
of the questions question number one get
the algebraic expressions in the
following cases using variables
constants and automatic operations
subtraction of Z from Y that is you are
subtracting Z from Y so you have
something like while and you subtract Z
from one so Y minus Z is the algebraic
expression number 5 added to 3 times the
product of numbers m and n so what would
be the product of M and n that would be
M into n which is MN 3 times the product
of M and n that is 3 into M in and what
is added to this number 5 that is 3 MN
plus 5 so this would be the desired
expression product of numbers y MZ
subtracted from 10 so product of ym
saiful to be by said and this is
subtracted from 10 that means 10 minus y
z sum of numbers a and b subtracted from
their product so sum of numbers a and b
would be a plus b and this a plus b is
subtracted from their product product is
KP so a B minus a plus B so that would
be the required expression question
number two identify terms and factors in
the expressions given below
so let us look at the first expression
which is 5x y square plus 7 X square Y
so how many terms does this expression
has it has two terms this is the first
term this is the second term because
these are the two parts which are added
to make this expression so the two terms
are 5x y squared + 7 X
we're why so these are the two terms we
also need to find out the factors now
let us first look at the factors here v
XY square so this v XY square can be
written as 5 into X into y into y so
these are all factors of 5 XY square
similarly 7 X square Y can be written as
7 into X into X into y so these are all
factors of 7 X square by so in this way
we wrote the terms and factors let's
look at the second expression which is 5
I plus 3 y square so how many terms are
present in this expression again here
also you have a 1 & 2 terms so the terms
for this expressions are 5y + 3 1 square
so these are the terms
what about factors when you look at 5 y
5 y can be written as 5 into y so 5 and
Y are the factors similarly 3 y square
can be written as 3 into y into y so the
three YY are the factors of 3 y square
so these are the various factors let us
now look at the third expression which
is 1.2 a B - 2 point 4 b + 3 point 6 8
so in this case how many parts do you
have 1 2 & 3 so what are the different
terms that you have the terms are 1.2 a
B - 2.4 B and 3.6 a so these are the
three terms what about the factors so
1.2 a B can be written as 1 point 2 into
a into B so these are the factors
similarly 2 - 2 point 4 B can be written
as
- 2.4 in to be so - 2.4 and be at the
factors
similarly 3.6 a can be written as 3
point 6 into a so basically 3 point 6 K
- 2.4 be 1 point - a B these are all
factors for this particular expression
so in this manner we find out the terms
and factors and this type of
representation of terms and factors is
called
the tree representation because the
terms and the factors are represented
like the branches of a tree so you have
first you have one branch and from there
you have two branches from these two
branches you again have two branches
each and so on so here also the
segregation happens in a similar way so
this is called a tree representation
question number three identify terms
which contain X and give the coefficient
of x so what is the expression 1 plus X
plus X by so when you look at this
expression that is 1 plus X plus X Y so
which are the terms with X so the terms
containing eggs are X and X Y so these
are the two terms which contain X now
what is the coefficient of x now we
cannot tell the coefficient of x in
general the coefficient of x in this
particular term so the coefficient of x
would be 1 in X that means in the first
term that is X what is the coefficient
of x nothing but 1 because 1 into X is X
so coefficient of x would be 1 in the
first term and what would be the
coefficient of x in the second term that
is in XY the coefficient would be
everything other than X that is y so the
coefficient of x would be Y in this term
X Y because as I have mentioned before
also that coefficient is always with
respect to a particular term let us look
at the second
which is 2 X square y minus 15 X Y
square plus 7y square so in this
expression we have to find out the terms
which contain by square so terms with y
square so which would be the terms with
y squares first term has Y naught Y
square but the second star term has Y
square so one term would be minus 15 X 5
square what about the third term this
also has Y square so the third term
would be 7 by square so what would be
the coefficient of Y square so the
coefficient of Y square in the first
term that isn't this term would be all
the term except Y square that is minus
15 X in this particular term that is
minus 15 X Y squared and what would be
the coefficient of Y square in this term
everything other than Y square that is 7
so the coefficient of Y squared will be
7 in the Dom 7 by square so in this
fashion we find out the coefficient of a
particular variable in a particular term
question number 4 classifying into
monomial binomial or trinomial first one
so how can you write the first
expression it can be written as 4 P
Square Q plus minus 4 P Q square so you
basically have two terms this is one
term and this is another term so
therefore this falls under the category
of binomial next one is Z square minus
3z plus 8 so how many terms do you have
three terms so this is an example of
trinomial here also you have a B minus a
minus B so here also you have three
terms so this is also an example of
trinomial hundred so hundred is just one
term we are not adding anything 200 so
this would be an example of moon
while square so this is also just one
term we are not adding or subtracting
anything from by square so this also is
an example of monomial question number
five state whether a given pair of terms
is of like or unlike tones so let's look
at the first pair we have minus 7x + 5
by 2x
now whenever we are comparing two terms
to find out if they are like or unlike
let us focus on the algebraic
coefficient or the algebraic part of the
factor so here there is every part is X
here there is every part is X again so
definitely these are like terms let's
look at the next pair which is 4 M
square P and for M P Square so again
let's focus on the algebraic part so
here the algebraic part is M square P
and here they are too big but is NP
square now both are different M square P
would mean M into M into P and MD square
would mean M into P into P so both are
different so therefore these are unlike
terms let's look at the third pair which
is 12 X Z and 12 X square Z square so
here was if you look at this algebra
part it is XZ if you look at this
algebraic part it is x squared z square
which is X into X + 2 Z into Z so here
also these are unlike terms thank you
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expressions part 7 is brought to you by
exam for calm no more fear from exam so
based on whatever we have learned so far
on algebraic expression their parts
their types let us have a look at some
of the questions question number one get
the algebraic expressions in the
following cases using variables
constants and automatic operations
subtraction of Z from Y that is you are
subtracting Z from Y so you have
something like while and you subtract Z
from one so Y minus Z is the algebraic
expression number 5 added to 3 times the
product of numbers m and n so what would
be the product of M and n that would be
M into n which is MN 3 times the product
of M and n that is 3 into M in and what
is added to this number 5 that is 3 MN
plus 5 so this would be the desired
expression product of numbers y MZ
subtracted from 10 so product of ym
saiful to be by said and this is
subtracted from 10 that means 10 minus y
z sum of numbers a and b subtracted from
their product so sum of numbers a and b
would be a plus b and this a plus b is
subtracted from their product product is
KP so a B minus a plus B so that would
be the required expression question
number two identify terms and factors in
the expressions given below
so let us look at the first expression
which is 5x y square plus 7 X square Y
so how many terms does this expression
has it has two terms this is the first
term this is the second term because
these are the two parts which are added
to make this expression so the two terms
are 5x y squared + 7 X
we're why so these are the two terms we
also need to find out the factors now
let us first look at the factors here v
XY square so this v XY square can be
written as 5 into X into y into y so
these are all factors of 5 XY square
similarly 7 X square Y can be written as
7 into X into X into y so these are all
factors of 7 X square by so in this way
we wrote the terms and factors let's
look at the second expression which is 5
I plus 3 y square so how many terms are
present in this expression again here
also you have a 1 & 2 terms so the terms
for this expressions are 5y + 3 1 square
so these are the terms
what about factors when you look at 5 y
5 y can be written as 5 into y so 5 and
Y are the factors similarly 3 y square
can be written as 3 into y into y so the
three YY are the factors of 3 y square
so these are the various factors let us
now look at the third expression which
is 1.2 a B - 2 point 4 b + 3 point 6 8
so in this case how many parts do you
have 1 2 & 3 so what are the different
terms that you have the terms are 1.2 a
B - 2.4 B and 3.6 a so these are the
three terms what about the factors so
1.2 a B can be written as 1 point 2 into
a into B so these are the factors
similarly 2 - 2 point 4 B can be written
as
- 2.4 in to be so - 2.4 and be at the
factors
similarly 3.6 a can be written as 3
point 6 into a so basically 3 point 6 K
- 2.4 be 1 point - a B these are all
factors for this particular expression
so in this manner we find out the terms
and factors and this type of
representation of terms and factors is
called
the tree representation because the
terms and the factors are represented
like the branches of a tree so you have
first you have one branch and from there
you have two branches from these two
branches you again have two branches
each and so on so here also the
segregation happens in a similar way so
this is called a tree representation
question number three identify terms
which contain X and give the coefficient
of x so what is the expression 1 plus X
plus X by so when you look at this
expression that is 1 plus X plus X Y so
which are the terms with X so the terms
containing eggs are X and X Y so these
are the two terms which contain X now
what is the coefficient of x now we
cannot tell the coefficient of x in
general the coefficient of x in this
particular term so the coefficient of x
would be 1 in X that means in the first
term that is X what is the coefficient
of x nothing but 1 because 1 into X is X
so coefficient of x would be 1 in the
first term and what would be the
coefficient of x in the second term that
is in XY the coefficient would be
everything other than X that is y so the
coefficient of x would be Y in this term
X Y because as I have mentioned before
also that coefficient is always with
respect to a particular term let us look
at the second
which is 2 X square y minus 15 X Y
square plus 7y square so in this
expression we have to find out the terms
which contain by square so terms with y
square so which would be the terms with
y squares first term has Y naught Y
square but the second star term has Y
square so one term would be minus 15 X 5
square what about the third term this
also has Y square so the third term
would be 7 by square so what would be
the coefficient of Y square so the
coefficient of Y square in the first
term that isn't this term would be all
the term except Y square that is minus
15 X in this particular term that is
minus 15 X Y squared and what would be
the coefficient of Y square in this term
everything other than Y square that is 7
so the coefficient of Y squared will be
7 in the Dom 7 by square so in this
fashion we find out the coefficient of a
particular variable in a particular term
question number 4 classifying into
monomial binomial or trinomial first one
so how can you write the first
expression it can be written as 4 P
Square Q plus minus 4 P Q square so you
basically have two terms this is one
term and this is another term so
therefore this falls under the category
of binomial next one is Z square minus
3z plus 8 so how many terms do you have
three terms so this is an example of
trinomial here also you have a B minus a
minus B so here also you have three
terms so this is also an example of
trinomial hundred so hundred is just one
term we are not adding anything 200 so
this would be an example of moon
while square so this is also just one
term we are not adding or subtracting
anything from by square so this also is
an example of monomial question number
five state whether a given pair of terms
is of like or unlike tones so let's look
at the first pair we have minus 7x + 5
by 2x
now whenever we are comparing two terms
to find out if they are like or unlike
let us focus on the algebraic
coefficient or the algebraic part of the
factor so here there is every part is X
here there is every part is X again so
definitely these are like terms let's
look at the next pair which is 4 M
square P and for M P Square so again
let's focus on the algebraic part so
here the algebraic part is M square P
and here they are too big but is NP
square now both are different M square P
would mean M into M into P and MD square
would mean M into P into P so both are
different so therefore these are unlike
terms let's look at the third pair which
is 12 X Z and 12 X square Z square so
here was if you look at this algebra
part it is XZ if you look at this
algebraic part it is x squared z square
which is X into X + 2 Z into Z so here
also these are unlike terms thank you
please visit exam fee or come for free
quality education you can learn with a
simple four-step learning process
wherein you can watch video lessons you
can ask your questions you can refer
notes and you can take a free online
test we have content for class 6 to 12
on physics chemistry mathematics and
biology along with practical videos so
please subscribe to our channel for
daily updates thank you
About this Video
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Dec 17, 2024 Last updated |
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