Question

Multiply the polynomial expression
(xy-2)(x^2+1)

Answer 1

To multiply the polynomial expressions \((xy - 2)(x^2 + 1)\), you can apply the distributive property (also known as the FOIL method for binomials).

Here's the step-by-step multiplication:

1. Distribute \(xy\) to both terms in the second polynomial:
\[
xy \cdot x^2 + xy \cdot 1 = xyx^2 + xy = x^3y + xy
\]

2. Now, distribute \(-2\) to both terms in the second polynomial:
\[
-2 \cdot x^2 + (-2) \cdot 1 = -2x^2 - 2
\]

3. Combine all of the terms:
\[
x^3y + xy - 2x^2 - 2
\]

Putting it all together, the result of multiplying the polynomials \((xy - 2)(x^2 + 1)\) is:
\[
\boxed{x^3y - 2x^2 + xy - 2}
\]