Question

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

Answer 1

To simplify the polynomial expression \((xy - 2)(x^2 + 1)\), we will use the distributive property (also known as the FOIL method for binomials). Here are the steps:

1. Distribute each term in the first factor \((xy - 2)\) to each term in the second factor \((x^2 + 1)\).

\[
(xy - 2)(x^2 + 1) = (xy)(x^2) + (xy)(1) - (2)(x^2) - (2)(1)
\]

2. Simplifying each term:

- \(xy \cdot x^2 = xyx^2 = x^3y\)
- \(xy \cdot 1 = xy\)
- \(-2 \cdot x^2 = -2x^2\)
- \(-2 \cdot 1 = -2\)

3. Combine all the simplified terms together:

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

So, the simplified expression is:

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