Question

Simplify the polynomial
expression
(xy − 2)(x^2 + 1). (2 points)

Answer 1

To simplify the expression \((xy - 2)(x^2 + 1)\), we can use the distributive property (also known as the FOIL method for binomials).

Let's distribute \(xy\) and \(-2\) across \(x^2 + 1\):

1. First, multiply \(xy\) by each term in \(x^2 + 1\):
\[
xy \cdot x^2 = xyx^2 = x^3y
\]
\[
xy \cdot 1 = xy
\]

2. Next, multiply \(-2\) by each term in \(x^2 + 1\):
\[
-2 \cdot x^2 = -2x^2
\]
\[
-2 \cdot 1 = -2
\]

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

Arranging it in standard form gives:
\[
x^3y - 2x^2 + xy - 2
\]

Thus, the simplified polynomial expression is:
\[
x^3y - 2x^2 + xy - 2
\]