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Answer
The expression \(9d - 81\) can be factored as \(9(d - 9)\).
Solution
We begin with the expression:
\[
9d - 81.
\]
**Step 1. Factor Out the Greatest Common Factor (GCF).**
Both terms, \(9d\) and \(81\), have a common factor of \(9\). Factor out \(9\):
\[
9d - 81 = 9\left(d\,-\,9\right).
\]
This is the fully factored form.
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Simplify this solution The Deep Dive
To factor the expression S^9 - 81, you can recognize this as a difference of squares. The formula for a difference of squares is a^2 - b^2 = (a + b)(a - b). Here, S^9 can be rewritten as (S^4.5)^2, and 81 as (9)^2. Therefore, the expression becomes ((S^4.5) + 9)((S^4.5) - 9). Additionally, you can further break down the second factor, (S^4.5) - 9, as it also presents a difference of squares, yielding: (S^4.5 + 9)(S^2.25 + 3)(S^2.25 - 3). Now, you have factored it into smaller components! Keep the factoring fun and keep exploring!
