(14+2/9s)(14+14s+1/9s)-(7+1/9s)^2
You asked:
Evaluate the expression: \(\left(14 + \frac{2}{9 s}\right) \cdot \left(14 + 14 s + \frac{1}{9 s}\right) - {\left( 7 + \frac{1}{9 s} \right)}^{2}\)
MathBot Answer:
Evaluated
\(\displaystyle \left(14 + \frac{2}{9 s}\right) \cdot \left(14 + 14 s + \frac{1}{9 s}\right) - {\left( 7 + \frac{1}{9 s} \right)}^{2} = - \left(7 + \frac{1}{9 s}\right)^{2} + \left(14 + \frac{2}{9 s}\right) \left(14 s + 14 + \frac{1}{9 s}\right) \)
Expanded
\[\left(14 + \frac{2}{9 s}\right) \cdot \left(14 + 14 s + \frac{1}{9 s}\right) - {\left( 7 + \frac{1}{9 s} \right)}^{2} = 196 s + \frac{1351}{9} + \frac{28}{9 s} + \frac{1}{81 s^{2}}\]
Factored
\[\left(14 + \frac{2}{9 s}\right) \cdot \left(14 + 14 s + \frac{1}{9 s}\right) - {\left( 7 + \frac{1}{9 s} \right)}^{2} = \frac{\left(63 s + 1\right) \left(252 s^{2} + 189 s + 1\right)}{81 s^{2}}\]