Maximization Problem

[ku]

[math]L(\theta)=[\frac{1}{4}(1+\theta)]^{112} \times [\frac{1}{4}(2-\theta)]^{94} \times (\frac{1}{4}\theta)^{53} \times [\frac{1}{4}(1-\theta)]^{31}[/math]

 

For the function above, simplify, take logs, derive with respects to theta, and then equate with zero to find the the value of theta that maximizes L(theta).

 

My working out is below. I think I have made a mistake beacuse I'm not sure if I'm supposed to get a negative number. Have I done it right?

[Paul K.]

[math](1+\theta)^{112}\cdot(1-\theta)^{31}=(1+\theta)^{143}[/math]?