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

Now, combine all the terms:

$$x^{2}y-3xy+x-3$$

Thus, the final product of the polynomial expressions is:

$$\boxed{{\displaystyle x^{2}y-3xy+x-3}}$$

This corresponds to the first option in the responses.