Question
implify the polynomial expression (y2−3)(xy+1) ANSWER
Answers
Answered by
GPT-4o mini
To simplify the polynomial expression \((y^2 - 3)(xy + 1)\), we can use the distributive property (also known as the FOIL method for binomials). We will distribute each term in the first polynomial to each term in the second polynomial.
1. Distributing \(y^2\):
- \(y^2 \cdot xy = xy^3\)
- \(y^2 \cdot 1 = y^2\)
2. Distributing \(-3\):
- \(-3 \cdot xy = -3xy\)
- \(-3 \cdot 1 = -3\)
Now, we combine all the terms together:
\[
(y^2 - 3)(xy + 1) = xy^3 + y^2 - 3xy - 3
\]
Now, we can write the finalized expression:
\[
xy^3 + y^2 - 3xy - 3
\]
Thus, the simplified polynomial expression is:
\[
xy^3 + y^2 - 3xy - 3
\]
1. Distributing \(y^2\):
- \(y^2 \cdot xy = xy^3\)
- \(y^2 \cdot 1 = y^2\)
2. Distributing \(-3\):
- \(-3 \cdot xy = -3xy\)
- \(-3 \cdot 1 = -3\)
Now, we combine all the terms together:
\[
(y^2 - 3)(xy + 1) = xy^3 + y^2 - 3xy - 3
\]
Now, we can write the finalized expression:
\[
xy^3 + y^2 - 3xy - 3
\]
Thus, the simplified polynomial expression is:
\[
xy^3 + y^2 - 3xy - 3
\]