• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer
  • ICSE Solutions
    • ICSE Solutions for Class 10
    • ICSE Solutions for Class 9
    • ICSE Solutions for Class 8
    • ICSE Solutions for Class 7
    • ICSE Solutions for Class 6
  • Selina Solutions
  • ML Aggarwal Solutions
  • ISC & ICSE Papers
    • ICSE Previous Year Question Papers Class 10
    • ISC Previous Year Question Papers
    • ICSE Specimen Paper 2021-2022 Class 10 Solved
    • ICSE Specimen Papers 2020 for Class 9
    • ISC Specimen Papers 2020 for Class 12
    • ISC Specimen Papers 2020 for Class 11
    • ICSE Time Table 2020 Class 10
    • ISC Time Table 2020 Class 12
  • Maths
    • Merit Batch

A Plus Topper

Improve your Grades

  • CBSE Sample Papers
  • HSSLive
    • HSSLive Plus Two
    • HSSLive Plus One
    • Kerala SSLC
  • Exams
  • NCERT Solutions for Class 10 Maths
  • NIOS
  • Chemistry
  • Physics
  • ICSE Books

What Are The Types Of Factorization

November 21, 2022 by Veerendra

Types Of Factorization Example Problems With Solutions

Type I: Factorization by taking out the common factors. 

Example 1:    Factorize the following expression
2x2y + 6xy2 + 10x2y2
Solution:    2x2y + 6xy2 + 10x2y2
=2xy(x + 3y + 5xy)

Type II: Factorization by grouping the terms.   

Example 2:    Factorize the following expression
a2 – b + ab – a
Solution:    a2 – b + ab – a
= a2 + ab – b – a = (a2 + ab) – (b + a)
= a (a + b) – (a + b) = (a + b) (a – 1)

Type III: Factorization by making a perfect square.  

Example 3:    Factorize of the following expression
9x2 + 12xy + 4y2
Solution:    9x2 + 12xy + 4y2
= (3x)2 + 2 × (3x) × (2y) + (2y)2
= (3x + 2y)2

Example 4:    Factorize of the following expression
\(\frac{{{x}^{2}}}{{{y}^{2}}}+2+\frac{{{y}^{2}}}{{{x}^{2\prime }}},x\ne 0,y\ne 0\)
Solution:    
Factorization-by-perfect-square-Example-1

Example 5:    Factorize of the following expression
\({{\left( 5x-\frac{1}{x} \right)}^{2}}+4\left( 5x-\frac{1}{x} \right)+4,x\ne 0\)
Solution:
Factorization-by-perfect-square-Example-2

People also ask:

  • Solving Quadratic Equations with Complex Roots
  • Factoring Quadratics
  • Solving Quadratic Equations by Factoring
  • Solving Factorable Quadratic Equations
  • Completing the Square
  • Solving Quadratic Equations by Completing the Square

Type IV: Factorizing by difference of two squares.

Example 6:    Factorize the following expressions
(a) 2x2y + 6 xy2 + 10 x2y2
(b) 2x4 + 2x3y + 3xy2 + 3y3
Solution:
Factorizing-by-difference-of-two-squares-example-1

Example 7:    Factorize 4x2 + 12 xy + 9 y2
Solution:
Factorizing-by-difference-of-two-squares-example-7

Example 8:    Factorize each of the following expressions
(i) 9x2 – 4y2
(ii) x3 – x
Solution:
Factorizing-by-difference-of-two-squares-example-8

Example 9:    Factorize each of the following expressions
(i) 36x2 – 12x + 1 – 25y2
\(\text{(ii) }{{a}^{2}}-\frac{9}{{{a}^{2}}},a\ne 0\)
Solution:
Factorizing-by-difference-of-two-squares-example-9

Example 10:    Factorize the following algebraic expression
x4 – 81y4
Solution:
Factorizing-by-difference-of-two-squares-example-10

Example 11:    Factorize the following expression
x(x+z) – y (y+z)
Solution:    x(x+z) – y (y+z) = (x2 – y2) + (xz–yz)
= (x–y) (x+y) + z (x–y)
= (x–y) {(x+y) + z}
= (x–y) (x+ y + z)

Example 12:    Factorize the following expression
x4 + x2 + 1
Solution:    x4 + x2 + 1 = (x4 + 2x2 +1) – x2
= (x2 +1)2 – x2 = (x2 + 1 – x) (x2 + 1+x)
= (x2–x + 1) (x2 + x + 1)

Type V: Factorizing the sum and difference of cubes of two quantities.
(i) (a3 + b3) = (a + b) (a2 – ab + b2)
(ii) (a3 – b3) = (a – b) (a2 + ab + b2)

Example 13:    Factorize the following expression
a3 + 27
Solution:   a3  + 27 = a3  + 33 = (a + 3) (a2 –3a +9)

Example 14:    Simplify : (x+ y)3 – (x –y)3 – 6y(x2 – y2)
Solution:    
factorizing-the-sum-and-difference-of-cubes

Filed Under: Mathematics Tagged With: Factorization, Factorization Examples, Polynomials, Types Of Factorization, Types Of Factorization With Example

Primary Sidebar

  • MCQ Questions
  • ICSE Solutions
  • Selina ICSE Solutions
  • Concise Mathematics Class 10 ICSE Solutions
  • Concise Physics Class 10 ICSE Solutions
  • Concise Chemistry Class 10 ICSE Solutions
  • Concise Biology Class 10 ICSE Solutions
  • Concise Mathematics Class 9 ICSE Solutions
  • Concise Physics Class 9 ICSE Solutions
  • Concise Chemistry Class 9 ICSE Solutions
  • Concise Biology Class 9 ICSE Solutions
  • ML Aggarwal Solutions
  • ML Aggarwal Class 10 Solutions
  • ML Aggarwal Class 9 Solutions
  • ML Aggarwal Class 8 Solutions
  • ML Aggarwal Class 7 Solutions
  • ML Aggarwal Class 6 Solutions
  • HSSLive Plus One
  • HSSLive Plus Two
  • Kerala SSLC
  • Recent Posts

    • Gurajada – The Legend Question and Answers
    • The Bond of Love Question and Answers
    • The Why – Why Girl Question and Answers
    • The Art of Weaving Question and Answers
    • The Brave Little Bowman Question and Answers
    • A Journey through the Hills and Valleys Question and Answers
    • The Turning Point Question and Answers
    • Painted House, Friendly Chicken and Me Question and Answers
    • AP 7th Class English TextBook Answers
    • 10 Lines on Mahatma Gandhi for Students and Children in English
    • Paragraph On Mahatma Gandhi 100, 150, 200, 250 to 300 Words for Kids, Students and Children

    Footer

    • Picture Dictionary
    • English Speech
    • ICSE Solutions
    • Selina ICSE Solutions
    • ML Aggarwal Solutions
    • HSSLive Plus One
    • HSSLive Plus Two
    • Kerala SSLC
    • Distance Education
    DisclaimerPrivacy Policy
    Area Volume Calculator