Easy Level Worksheet

Part A: Subjective Questions - Very Short Answer (1 Mark Each)

Factorisation is the reverse process of expansion, where we write an expression as a product of its factors.

Let's start by understanding common factors and basic factorisation techniques.

1. Define factorisation.

Factorisation is the process of writing an expression as a product of factorsthe process of writing an expression as a sum of factors.

Perfect! It's the reverse of multiplication or expansion.

2. Write any one method of factorisation.

Method: Common factor methodBy using identities

Excellent! Common factor method is the most basic technique.

3. Find the common factor of 6x and 9x².

Answer:

Correct! 3x divides both 6x and 9x².

4. Factorise: 4x + 8.

Answer: = (x + )

Great! 4x + 8 = 4(x + 2).

5. Find the common factors in 3x²y and 9xy².

Answer:

Perfect! 3xy is the HCF of both terms.

Drag each expression to its correct factorised form:

Part A: Section B – Short Answer Questions (2 Marks Each)

1. Factorise: 5x + 10y.

Common factor =

= ( + )

Excellent! 5x + 10y = 5(x + 2y).

2. Factorise: 8a²b + 4ab².

Common factor =

= ( + )

Perfect! 8a²b + 4ab² = 4ab(2a + b).

3. Factorise: 6x²y - 3xy².

Common factor =

= ( - )

Great! 6x²y - 3xy² = 3xy(2x - y).

4. Factorise: 15xy + 10x.

Common factor =

= ( + )

Excellent! 15xy + 10x = 5x(3y + 2).

5. Factorise: 9p²q + 12pq².

Common factor =

= ( + )

Perfect! 9p²q + 12pq² = 3pq(3p + 4q).

Part B: Objective Questions - Test Your Knowledge!

Answer these multiple choice questions:

6. 9a²b + 6ab² =

(a) 3ab(3a + 2b) (b) 9ab(2a + b) (c) 3b(3a + 2b) (d) 3a(3a + 2b)

Correct! HCF is 3ab, so 9a²b + 6ab² = 3ab(3a + 2b).

7. 12x²y - 6xy² =

(a) 6xy(2x - y) (b) 6xy(2y - x) (c) 12x(y - 2x) (d) 3x(4x - 2y)

Perfect! Common factor is 6xy, giving us 6xy(2x - y).

8. Common factor of 10a²b, 15ab², and 20ab is:

(a) 5a (b) 5ab (c) ab (d) 10ab

Excellent! HCF of all three terms is 5ab.

9. Factorisation is the reverse process of:

(a) Addition (b) Multiplication (c) Division (d) Subtraction

Correct! Factorisation is the reverse of multiplication/expansion.

10. Factorise 2x + 6 =

(a) 2(x + 3) (b) x(2 + 6) (c) 6(x + 2) (d) 2(x + 2)

Perfect! 2x + 6 = 2(x + 3).

🎉 Fantastic Work! You've Mastered Basic Factorisation!

Here's what you learned:

• Definition: Factorisation is writing an expression as a product of its factors

• Common Factor Method:

  1. Find the HCF (Highest Common Factor) of all terms
  2. Divide each term by the HCF
  3. Write as: HCF × (remaining expression)

• Finding HCF:

  • For coefficients: Find HCF of numbers (e.g., HCF of 6, 9 is 3)
  • For variables: Take lowest power (e.g., HCF of x², x³ is x)
  • Combine both

• Examples:

  • 6x + 9 = 3(2x + 3)
  • 4x²y + 8xy² = 4xy(x + 2y)
  • 15ab + 10a = 5a(3b + 2)

• Verification: Expand to check if you get the original expression

• Key Skill: Always look for the highest common factor first!

Factorisation is essential for solving equations and simplifying complex expressions!