How do you find 133 x 141 by being told that 137 squared is 18769?

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Cheng Jun Cheong

You can observe that 133 is 4 less than 137, and 141 is 4 more than 137. 133 = 137 - 4 141 = 137 + 4 Hence 133x141 = (137-4)(137+4). Notice that this is of the form (a+b)(a-b), which has a related identity: a^2 - b^2. (137-4)(137+4) = 137^2 - 4^2. Now just substitute in 137^2, and 4^2 is 16. And you have your answer.

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