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\left(xy-2\right)\left(x^{2}+1\right)
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GPT-4o mini
To expand the expression \((xy - 2)(x^2 + 1)\), we can use the distributive property (also known as the FOIL method for binomials). Let's break it down:
1. Distribute \(xy\) to both terms in the second factor \((x^2 + 1)\):
\[
xy \cdot x^2 + xy \cdot 1 = xyx^2 + xy = xy^1x^2 + xy = xy^1x^2 + xy = xyx^2 + xy
\]
2. Distribute \(-2\) to both terms in the second factor \((x^2 + 1)\):
\[
-2 \cdot x^2 + (-2) \cdot 1 = -2x^2 - 2
\]
3. Now, combine all the terms obtained from the distribution:
\[
xyx^2 + xy - 2x^2 - 2
\]
Therefore, the expanded form of \((xy - 2)(x^2 + 1)\) is:
\[
xyx^2 - 2x^2 + xy - 2
\]
This can also be written as:
\[
x^3y - 2x^2 + xy - 2
\]
1. Distribute \(xy\) to both terms in the second factor \((x^2 + 1)\):
\[
xy \cdot x^2 + xy \cdot 1 = xyx^2 + xy = xy^1x^2 + xy = xy^1x^2 + xy = xyx^2 + xy
\]
2. Distribute \(-2\) to both terms in the second factor \((x^2 + 1)\):
\[
-2 \cdot x^2 + (-2) \cdot 1 = -2x^2 - 2
\]
3. Now, combine all the terms obtained from the distribution:
\[
xyx^2 + xy - 2x^2 - 2
\]
Therefore, the expanded form of \((xy - 2)(x^2 + 1)\) is:
\[
xyx^2 - 2x^2 + xy - 2
\]
This can also be written as:
\[
x^3y - 2x^2 + xy - 2
\]
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