To solve the problem using the equation \( b \cdot 8 + 25 = 500 \), we can identify the operations involved:
- The term \( b \cdot 8 \) indicates that Niel uses multiplication to find out how many beads he used for the 8 necklaces.
- The \( + 25 \) indicates an addition because he is adding the 25 beads he bought to the total he had after making the necklaces.
The equation can be rearranged to solve for \( b \):
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Subtract 25 from both sides to isolate the term involving \( b \):
\( b \cdot 8 = 500 - 25 \) -
Finally, divide both sides by 8 to solve for \( b \):
\( b = \frac{500 - 25}{8} \)
Therefore, the operations needed to solve the problem are subtraction and division.
The correct response is:
- subtraction and division.