Video Transcript
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.
