The strategy
How it works
Split the number into tens and ones: (a + b).
Calculate a², 2ab, and b².
Add the three parts carefully.
See it in action
Worked examples
Example 123²
- 23 = 20 + 3.
- 20² = 400; 2 × 20 × 3 = 120; 3² = 9.
- 400 + 120 + 9 = 529.
Answer: 529
Example 231²
- 31 = 30 + 1.
- 30² = 900; 2 × 30 × 1 = 60; 1² = 1.
- 900 + 60 + 1 = 961.
Answer: 961
A quick heads-up
Common mistakes to avoid
- Leaving out the middle term 2ab; it accounts for both cross-products.
- Squaring the tens incorrectly; 20² is 400, not 40.
Your turn
Check your understanding
Choose an answer to see instant feedback and a short explanation. You can take the quiz again any time.
Question 1 of 3
What is 14²?
(10 + 4)² = 100 + 80 + 16 = 196.
What is the middle term when squaring 32?
For (30 + 2)², the middle term is 2 × 30 × 2 = 120.
What is 25²?
(20 + 5)² = 400 + 200 + 25 = 625.
Keep the momentum
Try a few practice problems
Choose a comfortable range and work through a short round with the free mental math trainer.