# Division of Algebraic Expression

In Algebra, the four basic arithmetic operations are addition, subtraction, multiplication, and division. An algebraic expression in Maths is an expression which is made up of constants, variables and arithmetic operators. We have learnt about addition, subtraction, multiplication of an algebraic expression. Here, we are going to discuss the division of an algebraic expression, which is an inverse process of multiplication. In this article, let us have a look at how the division of one expression by the other is carried out.

## Division of Monomial by a Monomial

A monomial is a polynomial which has only one term. The procedure to perform the division of monomial by another monomial is given below:

Consider an example, 6a^{3} ÷ 2a

Here 2a and 6a^{3} be the two monomials

The easiest way to perform the division of an algebraic expression is the cancellation of the common terms, which is similar to the division of the numbers.

6a^{3} ÷ 2a = (6 × a × a × a)/ 2 × a

Now, cancel out the common terms, we get

6a^{3} ÷ 2a = 3a^{2}

## Division of Polynomial by a Monomial

A polynomial may be a binomial, trinomial or with n-terms. Now, let us consider the division of a trinomial by a monomial.

(4a^{3} + 5a^{2} + 6a) ÷ 2a

Here, the trinomial is 4a^{3} + 5a^{2} + 6a, and monomial is 2a

From the trinomial, take the common factors. Here, 2a is the common term. Then, it becomes:

4a^{3} + 5a^{2} + 6a = 2a (2a^{2} + (5/2)a + 3)

Now, perform the division operation

(4a^{3} + 5a^{2} + 6a) ÷ 2a = [2a (2a^{2} + (5/2)a + 3)] / 2a

Now, cancel the term 2a in both the numerator and the denominator, then it becomes:

(4a^{3} + 5a^{2} + 6a) ÷ 2a = 2a^{2} + (5/2)a + 3

## Division of Polynomial by a Polynomial

Let us consider two polynomials to perform the division operation.

(7a^{2} + 14a) ÷ (a + 2)

Here, the two polynomials are in the binomial form.

Similar to the above process, take the common factors,

For the polynomial 7a^{2} + 14a , aa is the common factor. So, take “7a” as common, then it becomes,

7a^{2} + 14a = 7a(a+2)

Perform the division of algebraic operation,

(7a^{2} + 14a) ÷ (a + 2) = [7a(a+2)] / (a+2)

Cancel out (a+2) from both numerator and denominator, we get the solution for the division of an algebraic expression.

Thus, (7a^{2} + 14a) ÷ (a + 2) = 7a

### Division of Algebraic Expression Practice Problems

Solve the problems given below:

- Solve: 24(x
^{2}yz + xy^{2}z + xyz^{2}) by 8xyz - Divide: 7x
^{2}y^{2}z^{2 }÷ 14xyz - Divide: z(5z
^{2}– 80) by 5z(z + 4)

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