Factorize by Grouping The Terms
Factorize by grouping the terms (two or more) means that we need to group the terms which have common factors before factoring.
Method to factorize by grouping the terms:
(i) From the groups of the given expression a common factor can be taken out from each group.
(ii) Factorize each group
(iii) Now take out the factor common to group formed.
Now we will learn how to factorize by grouping two or more terms.
Solved examples to factorize by grouping the terms:
1. Factorize grouping the following expressions:
(i) 18a3b3 - 27a2b3 + 36a3b2
Solution:
18a3b3 - 27a2b3 + 36a3b2
= 9a2b2(2ab – 3b + 4a)
(ii) 12x2y3 - 21x3y2
Solution:
12x2y3 - 21x3y2
= 3x2y2(4y - 7x)
(iii) y3 - y2 + y - 1
Solution:
y3 - y2 + y - 1
= y2(y - 1) + 1(y - 1)
= (y - 1) (y2 + 1)
(iv) axy + bcxy – az – bcz
Solution:
axy + bcxy – az – bcz
= xy(a + bc) – z(a + bc)
= (a + bc) (xy – z)
(v) x2 - 3x – xy + 3y
Solution:
x2 - 3x – xy + 3y
= x(x - 3) - y(x - 3)
= (x - 3) (x – y)
2. How to factorize by grouping the following expressions?
Solution:
2x4 – x3 + 4x - 2
= x3(2x – 1) + 2(2x - 1)
= (2x – 1) (x3 + 2)
(ii) pr + qr - ps - qs
Solution:
pr + qr - ps - qs
= r(p + q) - s(p + q)
= (p + q) (r - s)
(iii) mx - my - nx - ny
Solution:
mx - my - nx - ny
= m(x - y) - n(x - y)
= (x - y) (m - n)
3. How to factorize by grouping the algebraic expressions?
(i) a2c2 + acd + abc + bdSolution:
a2c2 + acd + abc + bd
= ac(ac + d) + b(ac + d)
= (ac + d) (ac + b)
(ii) 5a + ab + 5b + b2
Solution:
5a + ab + 5b + b2
= a(5 + b) + b(5 + b)
= (5 + b) (a + b)
(iii) ab - by - ay + y2
Solution:
ab - by - ay + y2
= b(a - y) - y(a - y)
= (a - y) (b - y)
4. Factorize the expressions:
(i) x4 + x3 + 2x + 2Solution:
x4 + x3 + 2x + 2
= x3(x + 1) + 2 (x + 1)
= (x + 1) (x3 + 2)
(ii) f2x2 + g2x2 – ag2 – af2
Solution:
f2x2 + g2x2 – ag2 – af2
= x2(f2 + g2) – a (g2 + f2)
= x2(f2 + g2) – a(f2 + g2)
= (f2 + g2)(x2 – a)
5. Factorize by grouping the terms (a2 + 3a)2 - 2(a2 + 3a) – b(a2 + 3a) + 2b
Solution:
(a2 + 3a)2 - 2(a2 + 3a) – b(a2 + 3a) + 2b
= [(a2 + 3a)2 - 2(a2 + 3a)] – [b(a2 + 3a) - 2b]
= (a2 + 3a) (a2 + 3a - 2) – b(a2 + 3a - 2)
= (a2 + 3a - 2) (a2 + 3a - b)
8th Grade Math Practice
From Factorize by Grouping The Terms 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.
Recent Articles
-
Multiplication Table | Learn Tables from 0 – 25 | Multiplication Table
Jan 14, 25 11:09 PM
In math multiplication table we will learn the tables from 0 – 25. These multiplication tables help the students to learn the essential multiplication facts. Multiplication tables are very important f… -
3rd Grade Math Worksheets |3rd Grade Math Sheets|3rd Grade Math Lesson
Jan 14, 25 11:02 PM
3rd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students. Teachers and parents can also follow the worksheets to guide the students. -
3rd Grade Subtraction Worksheet | 3-Digit Subtraction Worksheets | Ans
Jan 14, 25 01:57 PM
In 3th Grade Addition Worksheet we will solve how to subtract 3-digit numbers by expansion, subtraction of 3-digit numbers without regrouping, subtraction of 3-digit numbers with regrouping, propertie… -
Facts about Subtraction | Subtraction of Small Numbers|Solved Examples
Jan 14, 25 12:29 AM
The operation to finding the difference between two numbers is called subtraction. Let us know some facts about subtraction which will help us to learn subtraction of large numbers. 1. Subtraction wit… -
Word Problems on Subtraction |Worksheet on Subtraction Word Problems |
Jan 14, 25 12:21 AM
In word problems on subtraction we need to read the question carefully and understand what we need to find out. We know, in subtraction the larger number from which we subtract the other number (the s…
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.