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).

Let's distribute each term in the first factor across each term in the second factor:

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

Now we calculate each term:

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

Now we can combine all these terms:

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

Therefore, the simplified polynomial expression is:

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

To fill in the blanks from your question:

- 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**.

Thus, in the blanks provided, the expressions would be as follows:
- _ \(1\)
- _ \(-2\)
- _ \(1\)
- _ \(-2\)