To simplify the polynomial expression \((y^2 - 3)(xy + 1)\), we will use the distributive property (also known as the FOIL method for binomials).
-
Distribute \(y^2\) across \((xy + 1)\): \[ y^2 \cdot xy + y^2 \cdot 1 = y^3x + y^2 \]
-
Distribute \(-3\) across \((xy + 1)\): \[ -3 \cdot xy - 3 \cdot 1 = -3xy - 3 \]
-
Now combine all the terms obtained from the above steps: \[ y^3x + y^2 - 3xy - 3 \]
So, the final simplified expression is: \[ y^3x - 3xy + y^2 - 3 \]
Thus, the simplified form of the polynomial expression is: \[ y^3x + y^2 - 3xy - 3 \]