Evaluate:
\[ \frac{37^3-28^3}{37^2+37\times28+28^2} \]
Solution:
Using identity:
\[ a^3-b^3=(a-b)(a^2+ab+b^2) \]
Here, \[ a=37,\qquad b=28 \]
\[ 37^3-28^3 = (37-28)(37^2+37\times28+28^2) \]
Substituting in the given expression:
\[ \frac{(37-28)(37^2+37\times28+28^2)} {37^2+37\times28+28^2} \]
\[ =37-28 \]
\[ =9 \]