<s>[INST] How does this expression simplification make sense? My simplification does not equal what is given. I attached an image of the expression I'm working with

I have no idea how $A(x)$ is simplified to $\displaystyle 5x - \left(\frac{1+\pi}{2}\right) x^2$.
Every time I work out the equation I get $$A(x) = 5x - x^2 - (\pi x^2/2) + \pi(x/2)^2$$
 [/INST] So, step-by-step
\begin{align*}
A(x)&=xy+\pi\left(\frac{x}{2}\right)^{2},\\&=x\left(5-x-\frac{\pi}{2}x\right)+\pi\left(\frac{x}{2}\right)^{2},\\&=5x-x^{2}-\frac{\pi}{2}x^{2}+\frac{\pi}{2^{2}}x^{2},\\&=5x+\left(\frac{\pi}{2^{2}}-\frac{\pi}{2}-1\right)x^{2},\\&=5x+\left(\frac{\pi}{2^2}-\frac{2\pi}{2^{2}}-\frac{2^{2}\cdot 1}{2^{2}\cdot 1}\right)x^{2},\\&=5x+\left(\frac{\pi-2\pi-2^{2}}{2^{2}}\right)x^{2},\\&=5x+\left(\frac{-2^{2}-\pi}{2^{2}}\right)x^{2},\\&=\boxed{5x-\left(\frac{2^{2}+\pi}{2^{2}}\right)x^{2}},\\&\not=5x-\left(\frac{1+\pi}{2}\right)x^{2}
\end{align*}
Hence the answer in your picture is wrong which is clear because in the second sign "$=$" they did not add the term $\pi\left(\frac{x}{2}\right)^{2}$ . You're correct in the simplification.
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