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Answer
The expression \( 49d^{2} - 81 \) can be factored as \( (7d - 9)(7d + 9) \).
Solution
We start by recognizing that the given expression is a difference of two perfect squares:
\[
49d^2 - 81 = (7d)^2 - 9^2.
\]
The difference of two squares can be factored using the formula:
\[
a^2 - b^2 = (a - b)(a + b).
\]
Here, \( a = 7d \) and \( b = 9 \). Applying the formula, we get:
\[
(7d - 9)(7d + 9).
\]
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Simplify this solution Mind Expander
To factor the expression \( 49 d^{2} - 81 \), we recognize it as a difference of squares. This specific form allows us to use the identity \( a^{2} - b^{2} = (a - b)(a + b) \). Here, \( a = 7d \) (since \( 49d^{2} = (7d)^{2} \)) and \( b = 9 \) (since \( 81 = 9^{2} \)). Using the identity, we can factor the expression as follows: \[ 49 d^{2} - 81 = (7d - 9)(7d + 9). \] Now you have it factored perfectly into two binomials!
