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

Question

.(2 points) fill in the blanks
_x3y+_x2+_xy+_

Answer 1

To simplify the polynomial expression \((xy - 2)(x^2 + 1)\), we will distribute \((xy - 2)\) to each term in \((x^2 + 1)\).

1. Distributing \(xy\): \[ xy \cdot x^2 = x^3y \] \[ xy \cdot 1 = xy \]

2. Distributing \(-2\): \[ -2 \cdot x^2 = -2x^2 \] \[ -2 \cdot 1 = -2 \]

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

Rearranging the terms, we get: \[ x^3y - 2x^2 + xy - 2 \]

Now filling in the blanks with the coefficients:

• 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 the filled blanks will be: 1, -2, 1, -2.