How much greater than $27^2$ is $43^2$ ?
To compare $27^2$ and $43^2$, I could try to find their actual values and subtract them, but that would involve some tedious arithmetic. Instead, I will use a shortcut based on the difference of squares formula: $(a^2 - b^2) = (a + b)(a - b)$. If I let $a = 43$ and $b = 27$, then I can write $(43^2 - 27^2) = (43 + 27)(43 - 27)$. Now, this is much easier to calculate, since I can do the additions and subtractions mentally. I get $(43^2 - 27^2) = (70)(16) = 1120$. This means that $43^2$ is $1120$ greater than $27^2$. 