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

Question

.(2 points)

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).

We distribute each term in the first polynomial by each term in the second polynomial:

1. Distributing \(xy\):

   • \(xy \cdot x^2 = xyx^2 = x^3y\)
   • \(xy \cdot 1 = xy\)

2. Distributing \(-2\):

   • \(-2 \cdot x^2 = -2x^2\)
   • \(-2 \cdot 1 = -2\)

Now, we combine all the results together:

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

Thus, the simplified polynomial expression is:

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

This is the final simplified form.