To calculate 43², we can write it as (40 + 3)².

Step-by-step solution

Idea: Split the number into a round number plus a small number. Squares of round numbers and small numbers are easy, so (a + b)² = a² + 2ab + b² turns a hard square into easy pieces.

1. Write 43 = 40 + 3, so a = 40 and b = 3.½ mark
2. 43² = (40 + 3)² = 40² + 2 × 40 × 3 + 3²½ mark
3. = 1600 + 240 + 9½ mark
4. = 1849½ mark

Check: 43 × 43 = 43 × 40 + 43 × 3 = 1720 + 129 = 1849 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Writing 43² = 40² + 3² = 1609. The middle term 2 × 40 × 3 = 240 is needed.
• Computing the middle term as 40 × 3 = 120 (forgetting the 2).
• Choosing an awkward split such as 43 = 30 + 13. It still works, but 40 + 3 keeps the arithmetic easy.

How this can come in the exam

Try one yourself

Find 71² using (a + b)² = a² + 2ab + b².

More questions like this

• Using the identity (a + b)² = a² + 2ab + b², expand the following:
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• The identity (a + b)² = a² + 2ab + b² can also be used to find factors of some algebraic expressions. Consider the algebraic expression x² + 4x + 4.
• Let us try to find factors of another algebraic expression: 36x² + 12x + 1.
• Let us try to factor 50p² + 60pq + 18q². What will a and b be in this case?

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