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 will use the distributive property (also known as the FOIL method for binomials).

1. Distribute \(xy\) to both terms in the second polynomial: \[ xy \cdot x^2 + xy \cdot 1 = x^3y + xy \]

2. Distribute \(-2\) to both terms in the second polynomial: \[ -2 \cdot x^2 + (-2) \cdot 1 = -2x^2 - 2 \]

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

So, the simplified form of the expression is: \[ x^3y - 2x^2 + xy - 2 \]

Now, filling in the blanks in the format provided:

• _x^3y
• _(-2)x^2
• _xy
• _(-2)

Thus, the completed answer is: _x^3y + _-2x^2 + _xy + _-2