# Factoring Terms by Regrouping

Factoring terms by regrouping (two or more) means that you need to rearrange the terms with common factors before factoring. In case of regrouping the terms of the given algebraic expression need to be arranged in suitable groups in such a way that all the groups have a common factor. After this arrangement factorization becomes easy.

Solved examples on factoring terms by regrouping:

1. Factorize the expression:

(i) a2x + abx + ac + aby + b2y + bc

Solution:

a2x + abx + ac + aby + b2y + bc

By suitably rearranging the terms, we have;

= a2x + abx + aby + b2y + ac + bc

= ax(a + b) + by(a + b) + c(a + b)

= (a + b) (ax + by + c)

(ii) p3k + p2(k – m) – p(m + n) – n

Solution:

p3k + p2(k – m) – p (m + n) – n

By suitably rearranging the terms, we have;

= p3k + p2k – p2m – pm – pn – n

= (p3k + p2k) – (p2m + pm) – (pn + n)

= p2k (p + 1) - pm (p + 1) – n (p + 1)

= (p + 1) (p2k – pm – n)

2. How to factorize by grouping the following expressions?

(i) ax – bx + by + cy – cx – ay

Solution:

ax – bx + by + cy – cx – ay

By suitably rearranging the terms, we have;

= ax - bx – cx – ay + by + cy

= x(a – b – c) - y(a – b – c)

(a – b – c) (x - y)

(ii) x3 - 2x2 + ax + x - 2a – 2

Solution:

x3 - 2x2 + ax + x - 2a – 2

By suitably rearranging the terms, we have;

= x3 - 2x2 + ax - 2a + x - 2

= (x3 - 2x2) + (ax - 2a) + (x - 2)

= x2(x - 2) + a(x - 2) + 1(x - 2)

= (x - 2) (x2 + a + 1)

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

1. ### Comparison of Three-digit Numbers | Arrange 3-digit Numbers |Questions

Sep 13, 24 02:48 AM

What are the rules for the comparison of three-digit numbers? (i) The numbers having less than three digits are always smaller than the numbers having three digits as:

2. ### Worksheet on Three-digit Numbers | Write the Missing Numbers | Pattern

Sep 13, 24 02:23 AM

Practice the questions given in worksheet on three-digit numbers. The questions are based on writing the missing number in the correct order, patterns, 3-digit number in words, number names in figures…

3. ### 2nd Grade Place Value | Definition | Explanation | Examples |Worksheet

Sep 13, 24 01:20 AM

The value of a digit in a given number depends on its place or position in the number. This value is called its place value.

4. ### Comparison of Two-digit Numbers | Arrange 2-digit Numbers | Examples

Sep 12, 24 03:07 PM

What are the rules for the comparison of two-digit numbers? We know that a two-digit number is always greater than a single digit number. But, when both the numbers are two-digit numbers