To match each quadratic equation to its factored form, let's first identify the standard forms of each quadratic equation based on their factors, and then we can see how they match up with the given factored forms.
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Factored Form: \((x+8)(x+8)\)
- This is \((x+8)^2\).
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Factored Form: \((x-16)(x+4)\)
- When expanded, this gives \(x^2 - 12x - 64\) (not a match).
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Factored Form: \((x+8)(x−8)\)
- This is the difference of squares: \(x^2 - 64\).
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Factored Form: \((x−8)(x−8)\)
- This is \((x-8)^2\) or \(x^2 - 16x + 64\).
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Factored Form: \((x+16)(x+4)\)
- When expanded, this gives \(x^2 + 20x + 64\) (not a match).
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Factored Form: \(x^2−64\)
- This is the difference of squares factored as \((x+8)(x−8)\).
Now let’s summarize the matching:
- \((x+8)(x+8)\) matches \((x+8)^2\).
- \((x−16)(x+4)\) does not have a straightforward match from the list of equations.
- \((x+8)(x−8)\) matches \(x^2−64\).
- \((x−8)(x−8)\) matches \((x-8)^2\).
- \((x+16)(x+4)\) does not have a straightforward match either.
- \(x^2−64\) matches with \((x+8)(x−8)\).
Final Matching:
- \((x+8)(x+8)\) : \((x+8)^2\)
- \((x+8)(x−8)\) : \(x^2-64\)
- \((x−8)(x−8)\) : \((x-8)^2\)
Please let me know if you need further assistance with any specific equations!