FACTORING BY GROUPING WORKSHEET
About "Factoring by grouping worksheet"
Factoring by grouping worksheet :
Here we are going to see some practice questions on factoring.
Factoring by grouping worksheet - Practice questions
(1) Factorise the following expression
2a3 - 3a2 b + 2a2 c
(2) Factorise the following expression
16x + 64x2y
(3) Factorise the following expression
10x3 + 25x4y
(4) Factorise the following expression
xy - xz + ay - az
(5) Factorise the following expression
p2 + pq + pr + qr
(6) Factorise the following expression
4a - 8b + 5ax - 10bx
Factoring by grouping worksheet - Solution
Question 1 :
Factorise the following expression
2a3 - 3a2 b + 2a2 c
Solution :
= 2a3 - 3a2 b + 2a2 c
In the above three terms, we have the common variable "a2".
By factor out "a2", we get
= a2 (2a - 3b + 2c)
Question 2 :
Factorise the following expression
16x + 64x2y
Solution :
= 16x + 64x2y
In the above two terms, we have the common term "16x".
By factor out "16x", we get
= x (16) + 16x (4xy)
= 16x (1 + 4xy)
Question 3 :
Factorise the following expression
10x3 + 25x4y
Solution :
= 10x3 + 25x4y
In the above two terms, we have the common term "5x3".
By factor out "5x3", we get
= 5x3 (2) + 5x3 (5xy)
= 5x3 (2 + 5xy)
Question 4 :
Factorise the following expression
xy - xz + ay - az
Solution :
= xy - xz + ay - az
Let us consider the first two terms as one group and third fourth terms as other group.
In the first two terms, we have the common variable "x".
In the third and fourth terms, we have the common variable "a"
= x (y - z) + a (y - z)
= (x + a) (y - z)
Question 5 :
Factorise the following expression
p2 + pq + pr + qr
Solution :
= p2 + pq + pr + qr
Let us consider the first two terms as one group and third fourth terms as other group.
In the first two terms, we have the common variable "p".
In the third and fourth terms, we have the common variable "r"
= p (p + q) + r (p + q)
= (p + r) (p + q)
Question 6 :
Factorise the following expression
4a - 8b + 5ax - 10bx
Solution :
= 4a - 8b + 5ax - 10bx
We have 4 terms in the given algebraic expression.Now we are going to split into two groups.
4a and -8b are in one group (Group 1)
5ax and -10bx are in the other group(Group 2)
Common term of 1st group is 4
Common term of 2nd group is 5x
= 4 (a - 2b) + 5x (a - 2b)
= (4 + 5x) (a - 2b)
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