The Method of Grouping Terms to find out the Common Factors in an expression is known as Factorization by Grouping. You can use this technique when there is no common factor between the terms so that you can split the expression into pairs and then find the factors for each of them. Refer to the following sections for finding different problems on factorization by grouping terms. Practice the Factorization by Grouping Terms Examples over here and learn how to factorize an expression by grouping terms.
Also, Read:
Grouping Method of Factorization Question and Answers
Example 1.
Find the factors by the grouping of terms: x2 – 3x – 3y + xy?
Solution:
Given Expression is x2 – 3x – 3y + xy
Rearranging the terms we have x2 – 3x + xy– 3y
= x(x-3)+y(x-3)
= (x+y)(x-3)
Therefore, factorization of expression x2 – 3x – 3y + xy by grouping the terms is (x+y)(x-3)
Example 2.
Factorize: 4x3 – 16x2 – x + 4?
Solution:
Given expression is 4x3 – 16x2 – x + 4
Rearranging the terms we have 4x3 – 16x2 – x + 4
=4x2(x-4)-1(x-4)
=(4x2-1)(x-4)
Therefore, factorization of expression 4x3 – 16x2 – x + 4 by grouping the terms method is (4x2-1)(x-4)
Example 3.
Factorize the following expression cx + cy + dx + dy
Solution:
Given Expression is cx + cy + dx + dy
Rearranging the terms and finding the common terms we have c(x+y)+d(x+y)
= (c+d)(x+y)
Factorization of expression cx + cy + dx + dy is (c+d)(x+y)
Example 4.
Factorize ax2 – bx2 + ay2 – by2 + az2 – bz2?
Solution:
Given Expression is ax2 – bx2 + ay2 – by2 + az2 – bz2
Rearranging the terms we can get common factors out i.e. x2(a – b) + y2(a – b) + z2(a – b)
= (a-b)(x2+y2+z2)
Factorization of expression ax2 – bx2 + ay2 – by2 + az2 – bz2 is (a-b)(x2+y2+z2)
Example 5:
Factorize 2x + 8y – 4px –16py?
Solution:
Given Expression is 2x + 8y – 4px –16py
Rearranging the terms we can bring out the common factors as follows 2(x+4y)-4p(x+4y)
= (2-4p)(x+4y)
Factorization of expression 2x + 8y – 4px –16py is (2-4p)(x+4y)
Example 6:
Factorize 6x2 – 17x + 12 by grouping?
Solution:
Given Expression is 6x2 – 18x + 12
Rearranging the terms we have 6x2 – 18x + 12 we have 6x2 – 12x -6x+ 12
= 6x(x-2)-6(x-2)
=(6x-6)(x-2)
Therefore, factoriation of expression 6x2 – 17x + 12 by grouping is (6x-6)(x-2)
Example 7:
Factorize the expression 2x2 + 5x + 2?
Solution:
Given Expression is 2x2 + 5x + 2
Rearranging them we can write as follows i.e. 2x2 + 4x + x+ 2
= 2x(x+2)+1(x+2)
= (2x+1)(x+2)
Therefore, 2x2 + 5x + 2 when factorized can be written as (2x+1)(x+2)
Example 8:
Factorize the trinomial by grouping 15u2 + 18uv + 20uv2 + 30v3?
Solution:
Given expression is 20u2 + 25uv + 24uv2 + 30v3
Rearranging them we can write as 5u(4u+5v)+6v2(4u+5v)
= (5u+6v2)(4u+5v)
Therefore, Factorization of Trinomial 15u2 + 18uv + 20uv2 + 30v3 is (5u+6v2)(4u+5v)