Multiply the polynominal expression (xy - 2)(x^2 + 1)

Question

? 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: \[ 1, -2, 1, -2 \]