Question
Simplify polinomial expression (xy-2)(x^2+1)
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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 will distribute each term in the first polynomial by each term in the second polynomial.
\[
(xy - 2)(x^2 + 1) = xy \cdot x^2 + xy \cdot 1 - 2 \cdot x^2 - 2 \cdot 1
\]
Now, perform the multiplication:
1. \(xy \cdot x^2 = xyx^2 = x^3y\)
2. \(xy \cdot 1 = xy\)
3. \(-2 \cdot x^2 = -2x^2\)
4. \(-2 \cdot 1 = -2\)
Now, combine all the results together:
\[
x^3y + xy - 2x^2 - 2
\]
Thus, the simplified expression is:
\[
x^3y + xy - 2x^2 - 2
\]
\[
(xy - 2)(x^2 + 1) = xy \cdot x^2 + xy \cdot 1 - 2 \cdot x^2 - 2 \cdot 1
\]
Now, perform the multiplication:
1. \(xy \cdot x^2 = xyx^2 = x^3y\)
2. \(xy \cdot 1 = xy\)
3. \(-2 \cdot x^2 = -2x^2\)
4. \(-2 \cdot 1 = -2\)
Now, combine all the results together:
\[
x^3y + xy - 2x^2 - 2
\]
Thus, the simplified expression is:
\[
x^3y + xy - 2x^2 - 2
\]
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