Question

Simplify the polynomial expression (xy - 2)(x ^ 2 + 1) . Box x ^ 3 * y + Box x^ 2 + Box xy+ Box

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):

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

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

Now, we combine all these results:
\[
x^3y + xy - 2x^2 - 2
\]

Rearranging gives us:
\[
x^3y - 2x^2 + xy - 2
\]

Now we can put the terms with common factors together if needed, but as the original expression seems to be structured into boxes, we can group the result:

- \(Box = x^3y\)
- \(Box = -2x^2\)
- \(Box = xy\)
- \(Box = -2\)

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