Subscribe to our YouTube channel for the latest videos, updates, and tips.


Monomial is a Common Factor

Factorization of algebraic expressions when a monomial is a common factor:
Factorization when a common monomial factor occurs in each term then;

(i) Write the algebraic expressions.

(ii) Find the H.C.F. of all the terms of the expression.

(iii) Divide each term of the expression by the H.C.F.

(iv) Keep the H.C.F. outside the bracket and the quotients obtained within the bracket.


Solved examples when a monomial is a common factor:

Factorize each of the following algebraic expressions.

(i) 10x + 15         

Solution:                 

10x + 15         

We can also write, 10x = 5 × 2x and 15 = 5 × 3

The H.C.F of 10x and 15 is 5           

Therefore, 10x + 15 = 5(2x + 3)                   


(ii) 9xy2 + 12x2y - 18xy

Solution:

9xy2 + 12x2y – 18xy

We can also write, 9xy2 = 3xy × 3y2, 12x2y = 3xy × 4x and 18xy = 3xy × 6

The H.C.F of the terms 9xy2, 12x2y, 18xy is 3xy.

Therefore, 9xy2 + 12x2y – 18xy = 3xy(3y + 4x – 6)

                                           = 3xy(4x + 3y – 6)


(iii) 12a2b - 9ab2 + 6ab

Solution:

12a2b - 9ab2 + 6ab

HCF of 12a2b, 9ab2, 6ab is 3ab.

Therefore, 12a2b - 9ab2 + 6ab

= 3ab(4a - 3b + 2).


(iv) 12m3 + 32m2n

Solution:

12m3 + 32m2n

HCF of 12m3 and 32m2n is 4m2.

Therefore, 12m3 + 32m2n = 4m2(3m + 8n).


8th Grade Math Practice

From Monomial is a Common Factor to HOME PAGE




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.



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.




Share this page: What’s this?

Recent Articles

RSS

  1. Worksheet on Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  2. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  3. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  4. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More

  5. Worksheet on Rounding Off Number | Rounding off Number | Nearest 10

    May 15, 25 05:12 PM

    In worksheet on rounding off number we will solve 10 different types of problems. 1. Round off to nearest 10 each of the following numbers: (a) 14 (b) 57 (c) 61 (d) 819 (e) 7729 2. Round off to

    Read More