1. The problem involves evaluating the expression $5x^3 - 3x^2 - 2(x - 10)^2$ at $x = -2$ and understanding the calculation steps. 2. The formula used is substitution into the polynomial and simplification: $$5x^3 - 3x^2 - 2(x - 10)^2$$ 3. Substitute $x = -2$: $$5(-2)^3 - 3(-2)^2 - 2(-2 - 10)^2$$ 4. Calculate powers: $$5(-8) - 3(4) - 2(-12)^2$$ 5. Multiply: $$-40 - 12 - 2 imes 144$$ 6. Calculate the last term: $$-40 - 12 - 288$$ 7. Sum all terms: $$-40 - 12 = -52$$ $$-52 - 288 = -340$$ 8. The confusion in the question seems to be about the step where $-40 - 12$ equals $-52$, which is correct, and the final total is $-340$, not $-52$. Final answer: $$-340$$