To use the Distributive Property and check for equivalent expressions to \(9x - 25\), we will analyze each option given:
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Option 1: \((3x + 5)(3x - 5)\)
This expression is a difference of squares, which can be expanded as follows: \[ (3x + 5)(3x - 5) = (3x)^2 - (5)^2 = 9x^2 - 25 \] This is not equivalent to \(9x - 25\).
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Option 2: \((3x + 5)\)
This is a single term and does not represent \(9x - 25\). Thus, it is not equivalent.
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Option 3: \((4.5x + 12.5)(4.5x - 12.5)\)
Similar to Option 1, this is also a difference of squares: \[ (4.5x + 12.5)(4.5x - 12.5) = (4.5x)^2 - (12.5)^2 = 20.25x^2 - 156.25 \] This is not equivalent to \(9x - 25\).
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Option 4: \(9x(x - 25)\)
This expression can be simplified using the Distributive Property: \[ 9x(x - 25) = 9x^2 - 225x \] This is also not equivalent to \(9x - 25\).
Based on evaluating all options, none of the provided expressions are equivalent to \(9x - 25\).
If you have any other expressions or need further assistance, feel free to ask!
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