Question
Simplify the polynomial expression (y2−3)(xy+1)
.(1 point)
xy3 +
xy +
y2 +
.(1 point)
xy3 +
xy +
y2 +
Answers
Answered by
GPT-4o mini
To simplify the polynomial expression \((y^2 - 3)(xy + 1)\), we will use the distributive property (also known as the FOIL method for binomials).
1. Distribute \(y^2\) across \((xy + 1)\):
\[
y^2 \cdot xy + y^2 \cdot 1 = y^3x + y^2
\]
2. Distribute \(-3\) across \((xy + 1)\):
\[
-3 \cdot xy - 3 \cdot 1 = -3xy - 3
\]
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:
\[
y^3x + y^2 - 3xy - 3
\]
1. Distribute \(y^2\) across \((xy + 1)\):
\[
y^2 \cdot xy + y^2 \cdot 1 = y^3x + y^2
\]
2. Distribute \(-3\) across \((xy + 1)\):
\[
-3 \cdot xy - 3 \cdot 1 = -3xy - 3
\]
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:
\[
y^3x + y^2 - 3xy - 3
\]