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

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

1 answer

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:

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