Factorization when Monomial is Common

In factorization when monomial is common factor we know, that an algebraic expression is the sum or the difference of monomials.

In order to factorize follow the following steps:

Step 1: Write the algebraic expression.

Step 2: Find the HCF of all the terms of the given algebraic expression.

Step 3:  Express each terms of the algebraic expression as the product of H.C.F and the quotient when it is divided by the H.C.F.

i.e. divide each term of the given expression by the HCF.

Step 4:  Now use distributive property of multiplication over addition or subtraction to express the algebraic expression as the product of H.C.F and the quotient of the expression divided by the H.C.F.

i.e. write the given expression as the product of this HCF and the quotient obtained in step 2. 

Step 5:  Keep the H.C.F. outside the bracket and the quotients obtained within the bracket.

Solved examples of factorization when monomial is common:

1. Factorize each of the following: 

(i) 5x + 20


5x + 20

= 5(x + 4)

(ii) 2n2 + 3n


2n2 + 3n

= n(2n + 3)

(iii) 3x2y - 6xy2


3x2y - 6xy2

= 3xy(x - 2y)

(iv) 6ab - 9bc


6ab - 9bc

= 3b(2a - 3c)

2. Factorize 6a2b2c + 27abc.


The H.C.F. of 6a2b2c and 27abc = (H.C.F. of 6 and 27) × (H.C.F. of a2b2c and abc)

The H.C.F. of 6 and 27 = 3

The H.C.F. of a2b2c and abc = abc

Therefore, the H.C.F. of 6a2b2c and 27abc is 3abc.

Now, 6a2b2c + 27abc = \(3abc(\frac{6a^{2}b^{2}c}{3abc} - \frac{27abc}{3abc})\)

                              = 3abc(2ab + 9)

Therefore, the factor of 6a2b2c + 27abc are 3abc and (2ab + 9).

3. Factorize the expression:

18a3 - 27a2b


18a3 - 27a2b

HCF of 18a3 and 27a2b is 9a2.

Therefore, 18a3 - 27a2b = 9a2(2a - 3b).

8th Grade Math Practice

From Factorization when Monomial is Common to HOME PAGE

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Share this page: What’s this?

Recent Articles

  1. Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

    Mar 02, 24 05:31 PM

    The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerato…

    Read More

  2. Subtraction of Fractions having the Same Denominator | Like Fractions

    Mar 02, 24 04:36 PM

    Subtraction of Fractions having the Same Denominator
    To find the difference between like fractions we subtract the smaller numerator from the greater numerator. In subtraction of fractions having the same denominator, we just need to subtract the numera…

    Read More

  3. Addition of Like Fractions | Examples | Worksheet | Answer | Fractions

    Mar 02, 24 03:32 PM

    Adding Like Fractions
    To add two or more like fractions we simplify add their numerators. The denominator remains same. Thus, to add the fractions with the same denominator, we simply add their numerators and write the com…

    Read More

  4. Comparison of Unlike Fractions | Compare Unlike Fractions | Examples

    Mar 01, 24 01:42 PM

    Comparison of Unlike Fractions
    In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare. To compare two fractions with different numerators and different denominators, we multiply by a nu…

    Read More

  5. Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples

    Feb 29, 24 05:12 PM

    Equivalent Fractions
    The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with re…

    Read More