Question

Multiply the polynominal expression (xy - 2)(x^2 + 1)
? X^3 y + ? x^2 + ? xy + ?

Answer 1

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

Let's expand the expression:

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

Now, perform the multiplications:

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, combine all the terms together:

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

Thus, the complete expression is:

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

To match your format \( ? X^3 y + ? x^2 + ? xy + ? \), we can fill in the coefficients for each term:
- 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, we have:

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

The final answer is:
\[
1, -2, 1, -2
\]