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

Question

.(2 points)
_x^3 y+_x2+_xy+_

Answer 1

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

1. Distribute \(xy\) across \(x^2 + 1\): \[ xy \cdot x^2 + xy \cdot 1 = xyx^2 + xy = x^3y + xy \]

2. Distribute \(-2\) across \(x^2 + 1\): \[ -2 \cdot x^2 + -2 \cdot 1 = -2x^2 - 2 \]

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

Putting it all together, the simplified form of the polynomial expression is:

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

Therefore, filling in the blanks for your polynomial expression:

• The coefficient for \(x^3y\) is 1.
• The coefficient for \(x^2\) is -2.
• The coefficient for \(xy\) is 1.
• The constant term is -2.

So the final answer is: \[ 1 , x^3 y - 2 , x^2 + 1 , xy - 2 \]