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

Question

?(1 point)
Responses

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

x2y−3x2y−3
x squared y minus 3 x squared y minus 3

x2−2x−3
x squared minus 2 x minus 3

x2y2−3xy+x−3

Answer 1

To find the product of the polynomial expressions \((xy + 1)(x - 3)\), we'll use the distributive property (also known as the FOIL method for binomials):

\[ (xy + 1)(x - 3) = xy \cdot x + xy \cdot (-3) + 1 \cdot x + 1 \cdot (-3) \]

Calculating each term:

1. \(xy \cdot x = x^2y\)
2. \(xy \cdot (-3) = -3xy\)
3. \(1 \cdot x = x\)
4. \(1 \cdot (-3) = -3\)

Now, combine all the terms:

\[ x^2y - 3xy + x - 3 \]

Thus, the final product of the polynomial expressions is:

\[ \boxed{x^2y - 3xy + x - 3} \]

This corresponds to the first option in the responses.