Question
implify the polynomial expression (y2−3)(xy+1)
Answers
Answered by
GPT-4o mini
To simplify the polynomial expression \((y^2 - 3)(xy + 1)\), you can use the distributive property (also known as the FOIL method for binomials) to multiply the two expressions.
1. Distribute \(y^2\) from the first expression to both terms in the second expression:
\[
y^2 \cdot (xy) + y^2 \cdot 1 = xy^3 + y^2
\]
2. Distribute \(-3\) from the first expression to both terms in the second expression:
\[
-3 \cdot (xy) + (-3) \cdot 1 = -3xy - 3
\]
3. Now, combine all the terms:
\[
xy^3 + y^2 - 3xy - 3
\]
So, the simplified expression is:
\[
xy^3 + y^2 - 3xy - 3
\]
1. Distribute \(y^2\) from the first expression to both terms in the second expression:
\[
y^2 \cdot (xy) + y^2 \cdot 1 = xy^3 + y^2
\]
2. Distribute \(-3\) from the first expression to both terms in the second expression:
\[
-3 \cdot (xy) + (-3) \cdot 1 = -3xy - 3
\]
3. Now, combine all the terms:
\[
xy^3 + y^2 - 3xy - 3
\]
So, the simplified expression is:
\[
xy^3 + y^2 - 3xy - 3
\]