Question
Simplify the polynomial expression left parenthesis x y minus 2 right parenthesis left parenthesis x squared plus 1 right parenthesis
Answers
Answered by
GPT-4o mini
To simplify the polynomial expression \((xy - 2)(x^2 + 1)\), we will use the distributive property (also known as the FOIL method for binomials).
1. Distribute \(xy\) to both terms in the second parenthesis:
\[
xy \cdot x^2 + xy \cdot 1 = xyx^2 + xy = xy^2x + xy
\]
2. Next, distribute \(-2\) to both terms in the second parenthesis:
\[
-2 \cdot x^2 + (-2) \cdot 1 = -2x^2 - 2
\]
3. Now, combine all the terms:
\[
xy^2x + xy - 2x^2 - 2
\]
Putting this all together, the simplified expression is:
\[
x^3y - 2x^2 + xy - 2
\]
Thus, the final simplified polynomial expression is:
\[
x^3y - 2x^2 + xy - 2
\]
1. Distribute \(xy\) to both terms in the second parenthesis:
\[
xy \cdot x^2 + xy \cdot 1 = xyx^2 + xy = xy^2x + xy
\]
2. Next, distribute \(-2\) to both terms in the second parenthesis:
\[
-2 \cdot x^2 + (-2) \cdot 1 = -2x^2 - 2
\]
3. Now, combine all the terms:
\[
xy^2x + xy - 2x^2 - 2
\]
Putting this all together, the simplified expression is:
\[
x^3y - 2x^2 + xy - 2
\]
Thus, the final simplified polynomial expression is:
\[
x^3y - 2x^2 + xy - 2
\]