Question

Use the Distributive Property to find the product. Choose the correct item from each drop-down menu to complete.

(x + y)(x – y) =
Choose...
2 –
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+
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–
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2
=
Choose...
2 –
Choose...
2

Answer 1

To use the Distributive Property to find the product \((x + y)(x - y)\), we can expand it step by step.

1. Distribute \(x\) to both \(x\) and \(-y\):
- \(x \cdot x = x^2\)
- \(x \cdot (-y) = -xy\)

2. 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:
\((x + y)(x - y) = x^2 - y^2\)