Question

(xy-2)(x squared+1) simplify

Answer 1

To simplify the expression \((xy - 2)(x^2 + 1)\), you can use the distributive property (also known as the FOIL method for binomials).

The expression is:

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

Distributing each term in the first binomial by each term in the second:

1. Multiply \(xy\) by \(x^2\):
\[
xy \cdot x^2 = xyx^2
\]

2. Multiply \(xy\) by \(1\):
\[
xy \cdot 1 = xy
\]

3. Multiply \(-2\) by \(x^2\):
\[
-2 \cdot x^2 = -2x^2
\]

4. Multiply \(-2\) by \(1\):
\[
-2 \cdot 1 = -2
\]

Now combine all these results:

\[
xyx^2 + xy - 2x^2 - 2
\]

This can be rearranged, but as is, the expression is simplified. The final result is:

\[
xyx^2 - 2x^2 + xy - 2
\]

Or, if you prefer to group similar terms, you can write it as:

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

So the simplified expression is:

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

Alternatively, keeping \(xyx^2\) as \(xyx^2\) is also valid.