Simplify $(\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2$

Analyze the question: We need to simplify the difference of two squares of expressions that look almost identical, differing only in the sign of 2.

Concept: Two methods work.

• Expand each bracket: (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².
• Or use the identity (a + b)² − (a − b)² = 4ab.

Solution:

Let a = √6 and b = 2.

Expanding:

• (√6 + 2)² = 6 + 4√6 + 4 = 10 + 4√6
• (√6 − 2)² = 6 − 4√6 + 4 = 10 − 4√6

Subtracting: (10 + 4√6) − (10 − 4√6) = 8√6

Check with the identity: 4ab = 4 × √6 × 2 = 8√6 ✓

Answer: The correct option is **C.

Tip: Whenever you see (a + b)² − (a − b)², go straight to 4ab. It saves time in JAMB, where every second counts. Similarly, (a + b)² + (a − b)² = 2(a² + b²).