2 products are built around the same midpoint: 74 × 76 and 73 × 77. Subtract the second from the first.

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Paired products around a midpoint

Mental mathHard

$2$ products are built around the same midpoint: $74 \times 76$ and $73 \times 77$ . Subtract the second from the first.

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Hint

Both products are symmetric around the same centre.

Solution

Both pairs are centred on $75$ .
Write $74 \times 76 = 7 5^{2} - 1^{2}$ , since $(75 - 1) (75 + 1) = 7 5^{2} - 1$ .
Write $73 \times 77 = 7 5^{2} - 2^{2}$ , since $(75 - 2) (75 + 2) = 7 5^{2} - 4$ .
The $7 5^{2}$ terms cancel, leaving $- 1 + 4 = 3$ .

Answer: $3$