Question

What is the product of the polynomial expression XY + 1 * x - 3

Answer 1

To find the product of the polynomial expression \( XY + 1 \) and \( x - 3 \), we will use the distributive property (also known as the FOIL method for binomials).

Let's denote the polynomials:
- \( A = XY + 1 \)
- \( B = x - 3 \)

Now we will multiply \( A \) and \( B \):

\[
(A)(B) = (XY + 1)(x - 3)
\]

Distributing each term in \( A \) by each term in \( B \):

1. First, distribute \( XY \) to both terms in \( B \):
\[
XY \cdot x = XYx
\]
\[
XY \cdot (-3) = -3XY
\]

2. Next, distribute the constant \( 1 \) to both terms in \( B \):
\[
1 \cdot x = x
\]
\[
1 \cdot (-3) = -3
\]

Now, combine all the results:
\[
XYx - 3XY + x - 3
\]

Thus, the product of the polynomial expression \( (XY + 1)(x - 3) \) is:
\[
XYx - 3XY + x - 3
\]

This expression can be rearranged or combined if needed, but as it stands, it is fully expanded.