1. **State the problem:** Simplify the expression $x^2 \binom{4}{y} \sum_{i=1}^{n} Fx^2$. 2. **Understand the components:** - $x^2$ is a squared variable. - $\binom{4}{y}$ is a binomial coefficient representing combinations of 4 items taken $y$ at a time. - $\sum_{i=1}^{n} Fx^2$ is a summation from $i=1$ to $n$ of the term $Fx^2$. 3. **Simplify the summation:** Since $F$ and $x^2$ do not depend on $i$, the summation is: $$\sum_{i=1}^{n} Fx^2 = n \cdot F x^2$$ 4. **Substitute back:** $$x^2 \binom{4}{y} \sum_{i=1}^{n} Fx^2 = x^2 \binom{4}{y} (n F x^2)$$ 5. **Combine like terms:** $$= n F x^2 \binom{4}{y} x^2 = n F \binom{4}{y} x^{2+2} = n F \binom{4}{y} x^4$$ 6. **Final simplified expression:** $$n F \binom{4}{y} x^4$$ This is the simplified form of the original expression.