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

Question

?(1 point)
Responses

x2−2x−3
x squared minus 2 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

x2y2−3xy+x−3
x squared y squared minus 3 x y plus x minus 3
Remaining Attempts : 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 \(xy\) to both terms in \((x-3)\): \[ xy \cdot x = x^2y \] \[ xy \cdot (-3) = -3xy \]

2. Distribute \(1\) to both terms in \((x-3)\): \[ 1 \cdot x = x \] \[ 1 \cdot (-3) = -3 \]

3. Combine all the results from the distributions: \[ x^2y - 3xy + x - 3 \]

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

From the options provided, the correct response is: x²y − 3xy + x − 3.