# Division of Algebraic Expressions

In algebra, **division** is one of the fundamental operations that we use to solve equations and understand the relationships between variables.

**Algebraic expressions** are mathematical statements that include variables (like ‘x’ or ‘y’), constants (numbers), and operators (addition, subtraction, multiplication, division).

In this article, we will discuss the division of algebraic expressions in simple terms.

**Division by a Constant **

When you divide an algebraic expression by a constant, you can make it easier by dividing each term by that constant.

**Example **

Divide (8x^2 – 16x) by 4.

First, divide each term by 4:

(8x^2 / 4) – (16x / 4) = 2x^2 – 4x

**Division by a Monomial **

When dividing by a monomial, you divide each term of the expression by that monomial.

**Example **

Divide (6y^2 – 18y) by 3y.

Start by multiplying by the 3y,

(6y^2 – 18y) / (3y) = (6y^2/ 3y – 18y/ 3y)

= 2y – 6

**Division by a Polynomial **

Dividing by a polynomial follows similar principles as division by a monomial.

**Example **

Divide (12x^3 – 6x^2 + 9x) by (3x^2).

Multiply each term by 3x^2,

(12x^3 – 6x^2 + 9x) / (3x^2) = (12x^3/ 3x^2 – 6x^2/ 3x^2 + 9x/ 3x^2)

= 4x – 2 + 3/x

**Solved Examples Division of Algebraic Expressions**

**Example**

Divide the algebraic expression (4x^2 – 12xy) by 4.

**Solution:**

To divide by a constant, you simply divide each term of the expression by that constant.

(4x^2 – 12xy) Ã· 4

= (4x^2 Ã· 4) – (12xy Ã· 4)

= x^2 – (12xy Ã· 4)

= x^2 -3xy

So, the result is: x^2 – 3xy.

### Example

Divide the algebraic expression (9x^3y^2 – 18x^2y) by 3x.

**Solution**

When dividing by a monomial, you divide each term of the expression by that monomial.

(9x^3y^2 – 18x^2y) Ã· 3x = (9x^3y^2 Ã· 3x) – (18x^2y Ã· 3x)

= 3x^2y^2- (18x^2y Ã· 3x)

= 3x^2y^2-6xy

So, the result is: 3x^2y^2 – 6xy.

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