To use the Distributive Property to find the product \((x + y)(x - y)\), we can expand it step by step.
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Distribute \(x\) to both \(x\) and \(-y\):
- \(x \cdot x = x^2\)
- \(x \cdot (-y) = -xy\)
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Distribute \(y\) to both \(x\) and \(-y\):
- \(y \cdot x = xy\)
- \(y \cdot (-y) = -y^2\)
Now, combine the results: \[ x^2 - xy + xy - y^2 \]
The \(-xy\) and \(xy\) cancel each other out: \[ x^2 - y^2 \]
Thus, the product is: \((x + y)(x - y) = x^2 - y^2\)
Now we can fill in the drop-down options:
- \(= \) \(x^2\)
- \( – \) \(y^2\)
- \(= \) \(x^2 - y^2\)
So the completed equation reads: \((x + y)(x - y) = x^2 - y^2\)