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

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

x2−2x−3

Answer 1

To find the product of the polynomial expressions $(xy+1)(x-3)$, we can use the distributive property (also known as the FOIL method in this case).

1. Distributing $xy$ to both terms in $(x-3)$:

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

2. Distributing $1$ to both terms in $(x-3)$:

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

Now we can combine all the products: $$x^{2}y-3xy+x-3$$

So, the correct product of the expressions $(xy+1)(x-3)$ is: $$x^{2}y-3xy+x-3$$

Thus, the answer is: x²y - 3xy + x - 3 (Response 1)