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Original Question
Simplify the polynomial expression (xy−2)(x2+1) .(2 points)
Simplify the polynomial expression (xy−2)(x^2+1)
.(2 points)
.(2 points)
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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).
We distribute each term in the first polynomial by each term in the second polynomial:
1. Distributing \(xy\):
- \(xy \cdot x^2 = xyx^2 = x^3y\)
- \(xy \cdot 1 = xy\)
2. Distributing \(-2\):
- \(-2 \cdot x^2 = -2x^2\)
- \(-2 \cdot 1 = -2\)
Now, we combine all the results together:
\[
x^3y + xy - 2x^2 - 2
\]
Thus, the simplified polynomial expression is:
\[
x^3y - 2x^2 + xy - 2
\]
This is the final simplified form.
We distribute each term in the first polynomial by each term in the second polynomial:
1. Distributing \(xy\):
- \(xy \cdot x^2 = xyx^2 = x^3y\)
- \(xy \cdot 1 = xy\)
2. Distributing \(-2\):
- \(-2 \cdot x^2 = -2x^2\)
- \(-2 \cdot 1 = -2\)
Now, we combine all the results together:
\[
x^3y + xy - 2x^2 - 2
\]
Thus, the simplified polynomial expression is:
\[
x^3y - 2x^2 + xy - 2
\]
This is the final simplified form.
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