Question

Simplify the polynomial expression (xy−2)(x^2+1)
.(2 points)
___x^3y+___x2+___xy+___

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). Here's how it works:

1. Distribute \(xy\) to every term in \((x^2 + 1)\):
- \(xy \cdot x^2 = x^3y\)
- \(xy \cdot 1 = xy\)

2. Distribute \(-2\) to every term in \((x^2 + 1)\):
- \(-2 \cdot x^2 = -2x^2\)
- \(-2 \cdot 1 = -2\)

Now, combine all the results:

\[
(xy - 2)(x^2 + 1) = x^3y + xy - 2x^2 - 2
\]

Now, we'll place it in the required format:

The simplified polynomial expression is:

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

So, filling in the blanks:
- ___x^3y: 1
- ___x^2: -2
- ___xy: 1
- ___: -2

Thus, the final answer is:
\[
1, -2, 1, -2
\]