Introduction to Monomials
A monomial is an algebraic expression in which there is no additional term in it. All the variables and constants are in product form. You will have a better understanding if you look at the following example –
The expression x 2, a x 2 y 2, a b c x 2 y 2 z 2 are monomials as there is no addition term in it. But if the above expression becomes x 2 + a x 2 y 2 +a b c x 2 y 2 z 2 then it no more remains a monomial. Now this expression will be called as a trinomial, which we are going to study later. In general, monomials come under the class of polynomial which is a very vast field of study.
Degree of a monomial is a sum of the exponents of all the variables used in the expression.
Now let’s perform some arithmetic operations based on monomials.
We are going to start up with addition.
In addition of monomials if we have similar variables, those which have same exponent value then their coefficients are added and the variable comes outside as a common term.
For Example – a x 3 y 2 – 5 b 3 x 3 y 2 + c 5 x 3 y 2 = ( a – 5 b 3 + c 5 ) x 3 y 2.
in the above equation we can see that the x 3 and y 2 are the variables present in all the three terms, so x 3 y 2 comes common and the rest is just added.
Now we move over to the multiplication of monomials. The powers of the same variable gets added and the constants are multiplied as usual.
For Example –
5 a x 3 z 8 ( – 7 a 3 x 3 y 2 ) = – 3 5 a 4 x 6 y 2 z 8.
So we can see that exponent of a = 1+3 = 4
exponent of x = 3+3= 6
exponent of y = 0+2 = 2
exponent of z = 8+0 = 8.
Just like in multiplication the exponents get added in a similar manner in division process the exponents get subtracted. For example.
35 a 4 x 3 z 9 : 7 a x 2 z 6 = 5 a 3 x z 3.
exponent of a = 4-1= 3
exponent of x = 3-2= 1
exponent of z = 9 -6 = 3.
Get the detailed knowledge of Binomials , Polynomial Solver and other math topics on Math Captain.com.
Processing your request, Please wait....
