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

  1. Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo

    Jul 25, 25 12:21 PM

    In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar…

    Read More

  2. Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox

    Jul 25, 25 03:15 AM

    Volume of a Cube and Cuboid
    We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:

    Read More

  3. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 24, 25 03:46 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More

  4. Volume of a Cube | How to Calculate the Volume of a Cube? | Examples

    Jul 23, 25 11:37 AM

    Volume of a Cube
    A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure i…

    Read More

  5. 5th Grade Volume | Units of Volume | Measurement of Volume|Cubic Units

    Jul 20, 25 10:22 AM

    Cubes in Cuboid
    Volume is the amount of space enclosed by an object or shape, how much 3-dimensional space (length, height, and width) it occupies. A flat shape like triangle, square and rectangle occupies surface on…

    Read More