Simplify the polynomial expression left parenthesis x y minus 2 right parenthesis left parenthesis x squared plus 1 right parenthesis

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).

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

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

3. Now, combine all the terms: \[ xy^2x + xy - 2x^2 - 2 \]

Putting this all together, the simplified expression is: \[ x^3y - 2x^2 + xy - 2 \]

Thus, the final simplified polynomial expression is: \[ x^3y - 2x^2 + xy - 2 \]