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Last updated at Sept. 11, 2018 by Teachoo
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Example 1 Find the square of the following numbers without actual multiplication. (i) 39 We know that 39 = 30 + 9 Now, 392 = 39 × 39 = (30 + 9) × (30 + 9) = 30 × (30 + 9) + 9 × (30 + 9) = 30 × 30 + (30 × 9) + (9 × 30) + 9 × 9 = 900 + 270 + 270 + 81 = 1521 Example 1 Find the square of the following numbers without actual multiplication. (ii) 42 We know that 42 = 40 + 2 Now, 422 = 42 × 42 = (40 + 2) × (40 + 2) = 40 × (40 + 2) + 2 × (40 + 2) = 40 × 40 + (40 × 2) + (2 × 40) + 2 × 2 = 1600 + 80 + 80 + 4 = 1764
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