11+ Entrance Exams

Asked by Yeeun

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

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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