Simplify the polynomial expression (xy-2) (x²+1)

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

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

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

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