**Factoring by grouping worksheet :**

Here we are going to see some practice questions on factoring.

(1) Factorise the following expression

2a^{3} - 3a^{2} b + 2a^{2} c

(2) Factorise the following expression

16x + 64x^{2}y

(3) Factorise the following expression

10x^{3} + 25x^{4}y

(4) Factorise the following expression

xy - xz + ay - az

(5) Factorise the following expression

p^{2} + pq + pr + qr

(6) Factorise the following expression

4a - 8b + 5ax - 10bx

**Question 1 :**

Factorise the following expression

2a^{3} - 3a^{2} b + 2a^{2} c

**Solution :**

= 2a^{3} - 3a^{2} b + 2a^{2} c

In the above three terms, we have the common variable "a^{2}".

By factor out "a^{2}", we get

= a^{2 }(2a - 3b + 2c)

**Question 2 :**

Factorise the following expression

16x + 64x^{2}y

**Solution :**

= 16x + 64x^{2}y

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

10x^{3} + 25x^{4}y

**Solution :**

= 10x^{3} + 25x^{4}y

In the above two terms, we have the common term "5x^{3}".

By factor out "5x^{3}", we get

= 5x^{3} (2) + 5x^{3} (5xy)

= 5x^{3} (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

p^{2} + pq + pr + qr

**Solution :**

= p^{2} + 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)

After having gone through the stuff given above, we hope that the students would have understood "Factoring by grouping worksheet".

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