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Simplify the polynomial expression (xy−2)(x2+1)
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Answers
Answered by
GPT-4o mini
To simplify the polynomial expression \( (xy - 2)(x^2 + 1) \), we can use the distributive property (also known as the FOIL method for binomials). We'll distribute each term in the first polynomial by each term in the second polynomial.
Starting with:
\[
(xy - 2)(x^2 + 1)
\]
Distributing \(xy\):
\[
xy \cdot x^2 + xy \cdot 1 = xy^3 + xy
\]
Next, distributing \(-2\):
\[
-2 \cdot x^2 - 2 \cdot 1 = -2x^2 - 2
\]
Now, we'll combine all the terms together:
\[
xy^3 + xy - 2x^2 - 2
\]
Rearranging the terms, we can write:
\[
xy^3 - 2x^2 + xy - 2
\]
Thus, the simplified form of the polynomial expression \( (xy - 2)(x^2 + 1) \) is:
\[
xy^3 - 2x^2 + xy - 2
\]
Starting with:
\[
(xy - 2)(x^2 + 1)
\]
Distributing \(xy\):
\[
xy \cdot x^2 + xy \cdot 1 = xy^3 + xy
\]
Next, distributing \(-2\):
\[
-2 \cdot x^2 - 2 \cdot 1 = -2x^2 - 2
\]
Now, we'll combine all the terms together:
\[
xy^3 + xy - 2x^2 - 2
\]
Rearranging the terms, we can write:
\[
xy^3 - 2x^2 + xy - 2
\]
Thus, the simplified form of the polynomial expression \( (xy - 2)(x^2 + 1) \) is:
\[
xy^3 - 2x^2 + xy - 2
\]