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

x2−2x−3
x squared minus 2 x minus 3

x2y−3x2y−3
x squared y minus 3 x squared y minus 3

x2y2−3xy+x−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).

Let's perform the multiplication step-by-step:

1. Multiply \(xy\) with \(x\): \[ xy \cdot x = x^2y \]

2. Multiply \(xy\) with \(-3\): \[ xy \cdot (-3) = -3xy \]

3. Multiply \(1\) with \(x\): \[ 1 \cdot x = x \]

4. Multiply \(1\) with \(-3\): \[ 1 \cdot (-3) = -3 \]

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

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

Therefore, the correct response is: x²y - 3xy + x - 3.