14xe^{\left(x-2\right)}-12e^{\left(x-2\right)}-7x^{3}+20x^{2}-26x+12
You asked:
Evaluate the expression: \(14 x {e}^{x - 2} - 12 {e}^{x - 2} - 7 {x}^{3} + 20 {x}^{2} - 26 x + 12\)
MathBot Answer:
Evaluated
\(\displaystyle 14 x {e}^{x - 2} - 12 {e}^{x - 2} - 7 {x}^{3} + 20 {x}^{2} - 26 x + 12 = - 7 x^{3} + 20 x^{2} + 14 x e^{x - 2} - 26 x - 12 e^{x - 2} + 12 \)
Expanded
\[14 x {e}^{x - 2} - 12 {e}^{x - 2} - 7 {x}^{3} + 20 {x}^{2} - 26 x + 12 = - 7 x^{3} + 20 x^{2} + \frac{14 x e^{x}}{e^{2}} - 26 x - \frac{12 e^{x}}{e^{2}} + 12\]
Factored
\[14 x {e}^{x - 2} - 12 {e}^{x - 2} - 7 {x}^{3} + 20 {x}^{2} - 26 x + 12 = - \left(7 x - 6\right) \left(x^{2} - 2 x - \frac{2 e^{x}}{e^{2}} + 2\right)\]
\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).