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

Question

?(1 point)
Responses

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

x2y−3xy+x−3
x squared y 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 use the distributive property (also called the FOIL method for binomials).

1. Distributing \( xy \) to both terms in \( (x-3) \): \[ xy \cdot x = x^2 y \quad \text{and} \quad xy \cdot (-3) = -3xy \]

2. Distributing \( 1 \) to both terms in \( (x-3) \): \[ 1 \cdot x = x \quad \text{and} \quad 1 \cdot (-3) = -3 \]

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

So the final product is: \[ x^2 y - 3xy + x - 3 \]

Looking at the responses given, the correct answer is: x²y - 3xy + x - 3.