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By factorizing or otherwise, evaluate (77)² − (23)².

By factorizing or otherwise, evaluate 77 squared minus 23 squared.

In this question, we are asked to evaluate an expression that is the difference between two square numbers by factoring or by using any other method. We could evaluate each operation by hand. However, it is easier to recall the formula for factoring a difference of two squares. We recall that the difference of squares formula tells us that 𝑎 squared minus 𝑏 squared is equal to 𝑎 minus 𝑏 times 𝑎 plus 𝑏. If we substitute 𝑎 equals 77 and 𝑏 equals 23 into this formula, then we obtain 77 squared minus 23 squared is equal to 77 minus 23 times 77 plus 23.

We now need to evaluate the expression inside each factor separately. We can calculate that 77 minus 23 is equal to 54. And we can also calculate that 77 plus 23 is equal to 100. Substituting these values into the expression gives us 54 times 100. We can evaluate this by recalling that we multiply a number by 100 by moving its digits two places to the left. Doing this gives us an answer of 5,400.

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