Simplify the polynomial expression (xy−2)(x2+1)

Question

.(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:

• _ \(1\)
• _ \(-2\)
• _ \(1\)
• _ \(-2\)