Factorisation of algebraic expressions: a² - b² = (a + b)(a - b)
Factorisation of algebraic expressions: a² + b² = (a + ib)(an - ib) where i = √(-1)
Factorisation of algebraic expressions: a³ - b³ = (a - b)(a² + ab + b²)
Factorisation of algebraic expressions: a³ + b³ = (a + b)(a² - ab + b²)
Factorisation of algebraic expressions: (x + y)² = x² + 2xy + y²
Factorisation of algebraic expressions: (x - y)² = x² - 2xy + y²

🪤 The 5 Mistakes That Cost Marks

Not checking if the given expression can be factorised using the identity a² - b² = (a + b)(a - b)
Not checking if the given expression can be factorised using the identity a² + b²
Not using the correct formula for factorising the difference of cubes: a³ - b³ = (a - b)(a² + ab + b²)
Not using the correct formula for factorising the sum of cubes: a³ + b³ = (a + b)(a² - ab + b²)
Not simplifying the expression after factorisation

✏️ 3 Solved PYQs

Question 1: Factorise: x² + 5x + 6 Step 1: We need to find two numbers whose product is 6 and sum is 5 Step 2: The two numbers are 2 and 3 Step 3: So we can write: x² + 5x + 6 = x² + 2x + 3x + 6 = x(x + 2) + 3(x + 2) = (x + 3)(x + 2)
Question 2: Factorise: x² - 7x + 12 Step 1: We need to find two numbers whose product is 12 and sum is -7 Step 2: The two numbers are -3 and -4 Step 3: So we can write: x² - 7x + 12 = x² - 3x - 4x + 12 = x(x - 3) - 4(x - 3) = (x - 4)(x - 3)
Question 3: Factorise: 9x² + 12x + 4 Step 1: We can see that 9x² = (3x)² and 4 = 2² Step 2: So we can write: 9x² + 12x + 4 = (3x)² + 2(3x)(2) + 2² = (3x + 2)²

🧠 The One Thing Most Students Get Wrong

Most students get wrong the factorisation of quadratic expressions ∈ the form of ax² + bx + c, where a ≠ 1
They try to factorise it by finding two numbers whose product is c and sum is b
However, this method only works when a = 1
When a ≠ 1, we need to use other methods such as splitting the middle term or using the quadratic formula

👁️ Ayush's Note

To factorise a quadratic expression ∈ the form of ax² + bx + c, first try to factorise it by finding two numbers whose product is ac and sum is b
If this method does not work, try splitting the middle term
If this method also does not work, try using the quadratic formula: x = (-b ± √(b² - 4ac))/(2a)

🔁 Last 5 Minutes Box

Factorisation of x² - y² = (x + y)(x - y)
Factorisation of x³ - y³ = (x - y)(x² + xy + y²)
Factorisation of x³ + y³ = (x + y)(x² - xy + y²)
Factorisation of x² + y² = (x + iy)(x - iy) where i = √(-1)
Factorisation of (x + y)² = x² + 2xy + y²

📝 Practice MCQs

1. Factorise: x² + 4x + 4

A) (x + 2)(x + 2)

B) (x + 1)(x + 3)

C) (x - 2)(x - 2)

D) (x - 1)(x - 3)

Answer: A) (x + 2)(x + 2)

2. Factorise: x² - 9x + 20

A) (x - 4)(x - 5)

B) (x + 4)(x + 5)

C) (x - 2)(x - 10)

D) (x + 2)(x + 10)

Answer: A) (x - 4)(x - 5)

3. Factorise: x² + x - 6

A) (x + 3)(x - 2)

B) (x - 3)(x + 2)

C) (x + 1)(x - 6)

D) (x - 1)(x + 6)

Answer: A) (x + 3)(x - 2)

4. Factorise: 4x² + 12x + 9

A) (2x + 3)²

B) (2x - 3)²

C) (2x + 1)²

D) (2x - 1)²

Answer: A) (2x + 3)²

5. Factorise: x² - 16x + 64

A) (x - 8)²

B) (x + 8)²

C) (x - 4)²

D) (x + 4)²

Answer: A) (x - 8)²

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This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

📚 Related Topics

Continue your revision with these related guides:

Factorisation of algebraic expressions: a² - b² = (a + b)(a - b)
Factorisation of algebraic expressions: a² + b² = (a + ib)(an - ib) where i = √(-1)
Factorisation of algebraic expressions: a³ - b³ = (a - b)(a² + ab + b²)
Factorisation of algebraic expressions: a³ + b³ = (a + b)(a² - ab + b²)
Factorisation of algebraic expressions: (x + y)² = x² + 2xy + y²
Factorisation of algebraic expressions: (x - y)² = x² - 2xy + y²