Simplify the polynomial expression (xy−2)(x2+1) .(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 in specific cases). We will distribute each term in the first polynomial to each term in the second polynomial.

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

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

Now, combining all these terms together, we have: \[ x^3y + xy - 2x^2 - 2 \]

The final simplified expression is: \[ \boxed{x^3y - 2x^2 + xy - 2} \]