Answer: A. $x^3 + 9x^2 - 3x + 40$

Explanation:1. Identify the given expression: $(x^3 + 4x^2 - 3x) + 5(x^2 + 8)$

2. Simplify the expression by distributing the $5$ in the second term: $5(x^2 + 8) = 5 \times x^2 + 5 \times 8 = 5x^2 + 40$

3. Substitute this back into the original expression: $x^3 + 4x^2 - 3x + 5x^2 + 40$

4. Combine like terms: - Terms with $x^3$: $x^3$ (only one term) - Terms with $x^2$: $4x^2 + 5x^2 = (4+5)x^2 = 9x^2$ - Terms with $x$: $-3x$ (only one term) - Constant terms: $40$ (only one term)

5. Write the simplified expression: $x^3 + 9x^2 - 3x + 40$

6. Compare with the given options (Source 332): - [A] $x^3 + 9x^2 - 3x + 40$ (Matches our result) - [B] $x^3 + 4x^2 - 3x + 40$ (Incorrect coefficient for $x^2$) - [C] $x^3 + 8x^2 - 3x + 40$ (Incorrect coefficient for $x^2$) - [D] $x^3 + 5x^2 - 3x + 40$ (Incorrect coefficient for $x^2$)

7. Conclusion: The equivalent expression is $x^3 + 9x^2 - 3x + 40$.