An algebraic expression consisting of only one term is called a monomial. It can be a product/quotient of variable and numerals or only variables or even constant terms.
Some of the examples are 3x^2, -p/2, 4xy, 63, -7z etc. Operations addition and subtraction cannot be used to represent a mono form as they are used when there are more than one term in an algebraic expression also monomials cannot have negative exponents. For instance 5-y, 7x+3, ab-3 are not mono forms.
The sum of the exponents of all the variables would be the degree of the same.
The degree of such a constant term is zero. To simplify monomials we would be using law of exponents, multiplication of mono forms and division of mono forms accordingly wherever required.
The order of operations is also followed while solving
The combination of these expressions which are given inside the parenthesis have to be simplified first.
If we have a power of an exponential algebraic expression then law of exponents is used. For example, given an expression (3a2b3)2 can be simplified by using the law of multiplying the exponents [(am)n=amn] giving 3a4b6
Multiplication of Monomials:
To multiply the given expression the exponents of the like terms are to be added using the law of exponents, am.an=am+n
Example: Given an expression 3x2y4. 4xy3 then we simplify applying the law of exponents am.an=am+n, we get 3.4 x2+1y4+3= 12x3y7
Example: -3(m2n).(-4mn3)
Coefficients are multiplied first and then the variable part
(-3.-4)(m2.m1)(n1.n3)=(12)(m2+1)(n1+3)= 12m3n4
Dividing monomials:
While dividing exponential expressions, the exponents of like terms are subtracted
Example: 9x3y4/3x2y this expression can be simplified applying the law of exponents am/an=am-n
We get, 3x3-2y4-1= 3xy3
Let us now learn the steps involved in solving monomials with the help of few examples as given below,
Example: -18a^3b^2c^5/3ab^2c
Here first the numeral part is simplified, -18/3= -6
Each of the like terms are simplified using the law of exponents,
a^3/a= a^3-1= a^2
b^2/b^2 = b^2-2=b0=1
c^5/c= c^5-1=c^4
Writing all the terms together we get, -6a^2c^4 which is the simplified form
I have recently faced lot of problem while learning Polynomial Formula, But thank to online resources of math which helped me to learn myself easily on net.
Example: Simplify (3p^2q3/3p) . (9p^2q^2/q^5)
First step would be to multiply the numerators and add the exponents of like terms
Numerator= (3.9)(p^2+2.q3+2) = 27p4q5
Then multiply the denominators and add the exponents of like terms if any
Denominator= (3.1)(p1q^5) [when the exponent is not given it is considered as 1]
Now divide the coefficients of the expression if possible
27/3 = 9
Next step would be to subtract the exponents of like terms
P4-1q5-5=p3.q0=p3.1=p3
The final answer is (3p^2q^3/3p).(9p^2q^2/q^5)= 9p^3
Some of the examples are 3x^2, -p/2, 4xy, 63, -7z etc. Operations addition and subtraction cannot be used to represent a mono form as they are used when there are more than one term in an algebraic expression also monomials cannot have negative exponents. For instance 5-y, 7x+3, ab-3 are not mono forms.
The sum of the exponents of all the variables would be the degree of the same.
The degree of such a constant term is zero. To simplify monomials we would be using law of exponents, multiplication of mono forms and division of mono forms accordingly wherever required.
The order of operations is also followed while solving
The combination of these expressions which are given inside the parenthesis have to be simplified first.
If we have a power of an exponential algebraic expression then law of exponents is used. For example, given an expression (3a2b3)2 can be simplified by using the law of multiplying the exponents [(am)n=amn] giving 3a4b6
Multiplication of Monomials:
To multiply the given expression the exponents of the like terms are to be added using the law of exponents, am.an=am+n
Example: Given an expression 3x2y4. 4xy3 then we simplify applying the law of exponents am.an=am+n, we get 3.4 x2+1y4+3= 12x3y7
Example: -3(m2n).(-4mn3)
Coefficients are multiplied first and then the variable part
(-3.-4)(m2.m1)(n1.n3)=(12)(m2+1)(n1+3)= 12m3n4
Dividing monomials:
While dividing exponential expressions, the exponents of like terms are subtracted
Example: 9x3y4/3x2y this expression can be simplified applying the law of exponents am/an=am-n
We get, 3x3-2y4-1= 3xy3
Let us now learn the steps involved in solving monomials with the help of few examples as given below,
Example: -18a^3b^2c^5/3ab^2c
Here first the numeral part is simplified, -18/3= -6
Each of the like terms are simplified using the law of exponents,
a^3/a= a^3-1= a^2
b^2/b^2 = b^2-2=b0=1
c^5/c= c^5-1=c^4
Writing all the terms together we get, -6a^2c^4 which is the simplified form
I have recently faced lot of problem while learning Polynomial Formula, But thank to online resources of math which helped me to learn myself easily on net.
Example: Simplify (3p^2q3/3p) . (9p^2q^2/q^5)
First step would be to multiply the numerators and add the exponents of like terms
Numerator= (3.9)(p^2+2.q3+2) = 27p4q5
Then multiply the denominators and add the exponents of like terms if any
Denominator= (3.1)(p1q^5) [when the exponent is not given it is considered as 1]
Now divide the coefficients of the expression if possible
27/3 = 9
Next step would be to subtract the exponents of like terms
P4-1q5-5=p3.q0=p3.1=p3
The final answer is (3p^2q^3/3p).(9p^2q^2/q^5)= 9p^3
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