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 \((x-3)\):

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

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

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

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

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

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