Question

Simplify the polynomial expression (xy−2)(x2+1)
.(2 points) fill in the blanks
_x3y+_x2+_xy+_

Answer 1

To simplify the polynomial expression \((xy - 2)(x^2 + 1)\), we will distribute \((xy - 2)\) to each term in \((x^2 + 1)\).

1. Distributing \(xy\):
\[
xy \cdot x^2 = x^3y
\]
\[
xy \cdot 1 = xy
\]

2. Distributing \(-2\):
\[
-2 \cdot x^2 = -2x^2
\]
\[
-2 \cdot 1 = -2
\]

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

Rearranging the terms, we get:
\[
x^3y - 2x^2 + xy - 2
\]

Now filling in the blanks with the coefficients:
- The coefficient of \(x^3y\) is **1**.
- The coefficient of \(x^2\) is **-2**.
- The coefficient of \(xy\) is **1**.
- The constant term is **-2**.

So the filled blanks will be:
**1**, **-2**, **1**, **-2**.