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Which of the following alternatives represents the correct expansion of the given square?

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(22)² = 20² + 80 + 80 + 2²

(43)² = 40² + 120 + 120 + 3²

(64)² = 60² + 120 + 120 + 4²

(71)² = 70² + 170 + 170 + 1²

answer is B.

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Detailed Solution

43 can be written as 43 = 40 + 3

∴ 43² = (40 + 3)²

= (40 + 3) × (40 + 3)

= 40 (40 + 3) + 3 (40 + 3)

= 40 × 40 + 40 × 3 + 3 × 40 + 3 × 3

= 40² + 120 + 120 + 3²

Thus, the square of the number 43 can be expressed as 43² = 40² + 120 + 120 + 3²_.

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