Question

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

___x^3y + ___x^2 + ___ xy + ___
Fill in blanks

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) to multiply the two expressions.

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

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

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

This simplifies to:
\[
x^3y - 2x^2 + xy - 2
\]

Now, let's fill in the blanks in your question:
___x^3y + ___x^2 + ___xy + ___

We have:
- 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, we fill in the blanks as follows:

1. 1
2. -2
3. 1
4. -2

So, the final answer is:
1 (for \(x^3y\)), -2 (for \(x^2\)), 1 (for \(xy\)), -2 (for the constant).