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−3x2y−3
x squared y minus 3 x squared y 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 can use the distributive property (also known as the FOIL method for binomials).

Let's distribute each term in \( (xy + 1) \) to \( (x - 3) \):

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

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

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

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

Now, combine all these results:

\[ x^2y - 3xy + x - 3 \]

So the product of the polynomial expressions \( (xy + 1)(x - 3) \) is:

\[ x^2y - 3xy + x - 3 \]

Looking at the response options provided, the correct choice is:

x²y - 3xy + x - 3 (or in your notation, \( x2y - 3xy + x - 3 \)).