a² - b² = (a + b)(a - b)
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
(a + b)³ = a³ + 3a²b + 3ab² + b³
(a - b)³ = a³ - 3a²b + 3ab² - b³
a³ + b³ = (a + b)(a² - ab + b²)
a³ - b³ = (a - b)(a² + ab + b²)
a² + b² = (a + b)² - 2ab
a² - b² = (a + b)(a - b)
(x + a)(x + b) = x² + (a + b)x + ab
(x - a)(x - b) = x² - (a + b)x + ab
(x + a)(x - b) = x² + (a - b)x - ab
(x - a)(x + b) = x² + (b - a)x - ab

🪤 The 5 Mistakes That Cost Marks

Not simplifying expressions before solving
Not factoring out common terms
Not using the correct formula for expansion
Not combining like terms
Not checking the answer by plugging it back into the original equation

✏️ 3 Solved PYQs

Solve: (2x + 5)(3x - 2) Step 1: Use the formula (a + b)(c + d) = ac + ad + bc + bd Step 2: Apply the formula: (2x + 5)(3x - 2) = 2x(3x) + 2x(-2) + 5(3x) + 5(-2) Step 3: Simplify: 6x² - 4x + 15x - 10 Step 4: Combine like terms: 6x² + 11x - 10
Solve: (x + 2)² Step 1: Use the formula (a + b)² = a² + 2ab + b² Step 2: Apply the formula: (x + 2)² = x² + 2(x)(2) + 2² Step 3: Simplify: x² + 4x + 4
Solve: x² - 16 Step 1: Use the formula a² - b² = (a + b)(a - b) Step 2: Apply the formula: x² - 16 = (x + 4)(x - 4)

🧠 The One Thing Most Students Get Wrong

Most students get wrong the expansion of (a + b)(a - b) as a² + b² instead of a² - b²
This mistake can be avoided by remembering the formula a² - b² = (a + b)(a - b)

👁️ Ayush's Note

Always remember to factor out common terms from expressions
Use the formula (a + b)(a - b) = a² - b² to simplify expressions
Always check the answer by plugging it back into the original equation

🔁 Last 5 Minutes Box

Last minute revision of formulas: a² - b² = (a + b)(a - b), (a + b)² = a² + 2ab + b²
Quick practice of simple questions: (x + 2)(x - 2), x² - 4
Revision of common mistakes: not simplifying expressions, not factoring out common terms

📝 Practice MCQs

1. What is the value of (2x + 3)(2x - 3)

A) 4x² - 9

B) 4x² + 9

C) 4x² - 6x - 9

D) 4x² + 6x + 9

Answer: A) 4x² - 9. Explanation: Using the formula a² - b² = (a + b)(a - b), we get (2x + 3)(2x - 3) = (2x)² - 3² = 4x² - 9

2. What is the value of (x + 2)²

A) x² + 4x + 4

B) x² - 4x + 4

C) x² + 2x + 4

D) x² - 2x - 4

Answer: A) x² + 4x + 4. Explanation: Using the formula (a + b)² = a² + 2ab + b², we get (x + 2)² = x² + 2(x)(2) + 2² = x² + 4x + 4

3. What is the value of x² - 16

A) (x + 4)(x - 4)

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

C) (x - 4)(x - 4)

D) (x + 2)(x - 2)

Answer: A) (x + 4)(x - 4). Explanation: Using the formula a² - b² = (a + b)(a - b), we get x² - 16 = (x + 4)(x - 4)

4. What is the value of (3x + 2)(2x - 1)

A) 6x² + 5x - 2

B) 6x² - 5x - 2

C) 6x² + x - 2

D) 6x² - x - 2

Answer: A) 6x² + 5x - 2. Explanation: Using the formula (a + b)(c + d) = ac + ad + bc + bd, we get (3x + 2)(2x - 1) = 3x(2x) + 3x(-1) + 2(2x) + 2(-1) = 6x² - 3x + 4x - 2 = 6x² + x - 2

5. What is the value of (x - 3)²

A) x² - 6x + 9

B) x² + 6x + 9

C) x² - 3x + 9

D) x² + 3x - 9

Answer: A) x² - 6x + 9. Explanation: Using the formula (a - b)² = a² - 2ab + b², we get (x - 3)² = x² - 2(x)(3) + 3² = x² - 6x + 9

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📚 Academic References

Content verified against peer-reviewed research:

A framework for entrepreneurial learning in higher education — Academic Journal (2016) 🔓 — DOI ↗
MIRA: An LLM-Driven Dual-Loop Architecture for Metacognitive Rewa... — Systems (2025) 🔓 — DOI ↗
Mathematical methods and human thought in the age of AI — ArXiv.org (2026) 🔓 — DOI ↗

🔓 = Open Access article

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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:

a² - b² = (a + b)(a - b)
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
(a + b)³ = a³ + 3a²b + 3ab² + b³
(a - b)³ = a³ - 3a²b + 3ab² - b³
a³ + b³ = (a + b)(a² - ab + b²)
a³ - b³ = (a - b)(a² + ab + b²)
a² + b² = (a + b)² - 2ab
a² - b² = (a + b)(a - b)
(x + a)(x + b) = x² + (a + b)x + ab
(x - a)(x - b) = x² - (a + b)x + ab
(x + a)(x - b) = x² + (a - b)x - ab
(x - a)(x + b) = x² + (b - a)x - ab