Difference of Squares?
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What is the difference of squares that is used to calculate the mini question?
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@tidyboar This is a good question! The trick is to notice that \(892\) and \(908\) are both centered around the number \(900.\) Whenever you are multiplying two numbers that are the same distance from a center number (an average), then this is a clear sign
that we can apply the difference of squares.\( 892 = 900 - 8 \)
\( 908 = 900 + 8 \)Even better, we know that we can very easily square \(900\) and we can also easily square \(8.\)
So, instead of writing our product as \(892\) and \(908,\) we can write it as \( (900 - 8)(900 + 8 )\), which is a lot easier to figure out because we can expand and cancel the cross terms.
$$\begin{aligned} (900 - 8)(900 + 8 ) &= 900^2 + \textcolor{red}{(900)(8) - (900)(8)} - 8^2 \\ &= \boxed{900^2 - 8^2} \end{aligned} $$
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@debbie thanks!
