To solve the equation \( b \times 8 + 25 = 500 \), where \( b \) represents the number of beads Niel started with, you can identify the operations involved in the solution process:
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Subtraction: To isolate the term involving \( b \), you would first subtract 25 from both sides of the equation: \[ b \times 8 = 500 - 25 \]
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Division: After simplifying the equation, you would divide by 8 to solve for \( b \): \[ b = \frac{500 - 25}{8} \]
Thus, the operations needed to solve the problem are subtraction and division.
The correct response is: subtraction and division.