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

Question

?(1 point)
Responses

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
x squared y minus 3 x squared y 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 for binomials):

1. Distribute \(xy\) through \((x - 3)\):

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

2. Distribute \(1\) through \((x - 3)\):

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

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

Thus, the product of the polynomial expressions \((xy + 1)(x - 3)\) is: \[ x^2y - 3xy + x - 3 \]

The correct response is: x²y − 3xy + x − 3