This Unit is for Grade VII, here we are going to learn about monomials operations. A monomial is an algebraic expression which has only one term. Now we will learn about Operations on monomials. All mathematical operators namely addition, subtraction, multiplication and division can be performed on monomials. Before we discuss the methods of operation we must know the terms like terms and unlike terms. The terms with same variables are called like terms as 2xy and 5yx are like terms, on another hand 3xz and 3x are unlike terms.ely, without considering if they are like terms or not
When we perform addition and subtraction of the two monomials, then we add the terms which are like and the unlike terms are simply written in original form with their operators. If the two monomials are multiplied or divided, we perform the operation of multiplication with constants and the variables separately
Addition and subtraction of monomials is possible with like terms only, if the terms are unlike, then only the terms are represented as follows:
Add 3xy and 4xz will give 3xy + 4xz Ans
On another hand if we have to add 4x , 3y and 8x, we get
=4x + 3y + 8x
= 4x + 8x + 3y = 12x + 3y Ans.
Now we take the problem of subtraction: Find the difference between 6x and 2x will give:
= 6x – 2x = 4x Ans
If the problem is as follows Subtract 4x from 6y, we get
6y – 4x Ans as the two monomial terms are not like. (know more about cbse board papers, here)
In case of multiplication, we can multiply the terms without considering if they are like or unlike. In multiplication, the numerals of the two monomials are multiplied and the powers of the like variables are added up. Similarly when we divide one monomial with another, in that too we need not to have like terms. We will simply divide the numeral with the numeral and the powers of the same variables are subtracted. Let us make it more clear with the following examples:
Multiply 4x2y and 3y, we can write the above expression as = 4x2y * 3y =4 * 3 * x2y * y
= 12 x2y2.
Divide 12x2y and 3y, we can write the above expression as = 12x2y / 3y = (12/3)* x2 * y1-1.
= 4 x2 * y0 , but we know that any number raise to the power 0 is 1, we get 4 x2 Ans
In The Next Session We Are Going To Discuss Linear non-linear functions.
When we perform addition and subtraction of the two monomials, then we add the terms which are like and the unlike terms are simply written in original form with their operators. If the two monomials are multiplied or divided, we perform the operation of multiplication with constants and the variables separately
Addition and subtraction of monomials is possible with like terms only, if the terms are unlike, then only the terms are represented as follows:
Add 3xy and 4xz will give 3xy + 4xz Ans
On another hand if we have to add 4x , 3y and 8x, we get
=4x + 3y + 8x
= 4x + 8x + 3y = 12x + 3y Ans.
Now we take the problem of subtraction: Find the difference between 6x and 2x will give:
= 6x – 2x = 4x Ans
If the problem is as follows Subtract 4x from 6y, we get
6y – 4x Ans as the two monomial terms are not like. (know more about cbse board papers, here)
Multiply 4x2y and 3y, we can write the above expression as = 4x2y * 3y =4 * 3 * x2y * y
= 12 x2y2.
Divide 12x2y and 3y, we can write the above expression as = 12x2y / 3y = (12/3)* x2 * y1-1.
= 4 x2 * y0 , but we know that any number raise to the power 0 is 1, we get 4 x2 Ans
In The Next Session We Are Going To Discuss Linear non-linear functions.
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