Answer:
(d - 4)² - 7
Explanation:
Formula for completing the square: x² + ax + b = (x + )² - ()² + b
d² - 8d + 9 = (d - )² - ()² + 9
= (d - 4)² - 4² + 9
= (d - 4)² - 16 + 9
= (d - 4)² - 7
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)² - ()² + b 
)² - ()² + 9