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

Question

.(2 points)
___x^3y+___x^2+___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 multiply each term in the first binomial by each term in the second binomial.

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

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

Now, combining all the terms we obtained: \[ x^3y + xy - 2x^2 - 2 \]

Now, rearranging the expression in standard form: \[ x^3y - 2x^2 + xy - 2 \]

So, the simplified polynomial expression is: \[ \boxed{x^3y - 2x^2 + xy - 2} \]

When filling in the blanks:

• 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, the final answer is:

1. 1
2. -2
3. 1
4. -2