Which is the product of the polynomial expressions (xy+1)(x−3)

Question

?(1 point)
Responses

x2−2x−3
x squared minus 2 x minus 3

x2y2−3xy+x−3
x squared y squared minus 3 x y plus x minus 3

x2y−3xy+x−3
x squared y minus 3 x y plus x minus 3

x2y−3x2y−3

Answer 1

To find the product of the polynomial expressions \( (xy + 1)(x - 3) \), we need to distribute each term in the first expression across the terms in the second expression.

1. Distributing \( xy \) across \( (x - 3) \):

   • \( xy \cdot x = x^2y \)
   • \( xy \cdot (-3) = -3xy \)

2. Distributing \( 1 \) across \( (x - 3) \):

   • \( 1 \cdot x = x \)
   • \( 1 \cdot (-3) = -3 \)

Now, we can combine all the results: \[ x^2y - 3xy + x - 3 \]

So the final product is: \[ x^2y - 3xy + x - 3 \]

Thus, the correct response is: x²y - 3xy + x - 3.