1. The problem is to simplify the expression $3x^3 + 7x - 4 (Fq + 2)^2$. 2. We start by understanding the expression: it contains a cubic term $3x^3$, a linear term $7x$, and a product of $-4$ with the square of $(Fq + 2)$. 3. The formula for squaring a binomial is $$(a + b)^2 = a^2 + 2ab + b^2$$. 4. Applying this to $(Fq + 2)^2$, we get $$Fq^2 + 2 \times Fq \times 2 + 2^2 = Fq^2 + 4Fq + 4$$. 5. Now multiply this by $-4$: $$-4(Fq^2 + 4Fq + 4) = -4Fq^2 - 16Fq - 16$$. 6. Substitute back into the original expression: $$3x^3 + 7x - 4Fq^2 - 16Fq - 16$$. 7. This is the simplified form of the expression. Final answer: $$3x^3 + 7x - 4Fq^2 - 16Fq - 16$$