Question

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

(So it fits into the boxes)
□x³y+□x²+□xy+□

Answer 1

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

\[
(xy - 2)(x^2 + 1) = xy \cdot x^2 + xy \cdot 1 - 2 \cdot x^2 - 2 \cdot 1
\]

Now, we simplify 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, combine all the terms:

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

Now, let's write it in the specified format:

\[
\boxed{1}x^3y + \boxed{-2}x^2 + \boxed{1}xy + \boxed{-2}
\]

So, filling the boxes with the coefficients from the simplified expression, we have:

1. For \(x^3y\), the coefficient is **1**.
2. For \(x^2\), the coefficient is **-2**.
3. For \(xy\), the coefficient is **1**.
4. For the constant term, the coefficient is **-2**.

Thus, the filled boxes are:

\[
1, -2, 1, -2
\]