Question

Simplify the polynomial expression (xy−2)(x2+1)
.(2 points)
x3y+
x2+
xy+

Answer 1

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

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

Now, we can calculate each term:

1. \(xy \cdot x^2 = x^3y\)
2. \(xy \cdot 1 = xy\)
3. \(-2 \cdot x^2 = -2x^2\)
4. \(-2 \cdot 1 = -2\)

Putting it all together, we get:

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

So, the simplified form of the polynomial expression \((xy - 2)(x^2 + 1)\) is:

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

Thus, if we write the final result with coefficients as you requested, we can represent it like this:

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

So the simplified expression does not require more than what was computed; it is already presented in a simplified manner.

In summary, the simplified expression is:

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