Division of Algebraic Expressions

Introduction to division of algebraic expressions

There are four ways to divide an algebraic expression by another expression:

i) Dividing a monomial by monomial

ii) Dividing a polynomial by monomial

iii) Dividing a binomial by monomial

iv) Dividing a polynomial by polynomial

Division of an algebraic expression by a monomial

i) Division of a monomial by another monomial:

A monomial 40xy 2 is divided by another monomial 10y will result in 40xy2 /10y=4xy.

The result of dividing a monomial by another monomial will be a monomial.

ii) Division of a polynomial by a monomial:

Divide each term of the polynomial by the monomial to get the result of the division.

A polynomial −12xyz 3+60 is divided by a monomial 4z will result in: 3xyz 2+15z

Dividing any polynomial by a monomial will result in a polynomial.

The relation between the power of exponents and division of an algebraic expression by another algebraic expression:

The above law of exponents can be used to divide an algebraic expression by another, for instance: 4xy 2/2y=2xy 2−1  =2xy

Finding error

Let us look at the division of algebraic expression: (3x+2)/2=3x 

when the numerator is connected by the terms we cannot directly cancel the values from numerator and denominator.

Example:

Let us look for some general error that we have done while solving the exercises involves algebraic expressions.

1. 3(x+2)=3x+2 - In this case, we need to apply distributive law to find the result. The number 3 should be multiplied over both the values inside the bracket. That is 3x+6.

2. 6x+2y=8xy - In this case, we cannot add the terms with different variable.