To simplify the polynomial expression \((xy - 2)(x^2 + 1)\), we will use the distributive property (also known as the FOIL method for binomials).
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Distribute \(xy\): \[ xy \cdot x^2 = x^3y \] \[ xy \cdot 1 = xy \]
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Distribute \(-2\): \[ -2 \cdot x^2 = -2x^2 \] \[ -2 \cdot 1 = -2 \]
Now, combine all these results:
\[ x^3y + xy - 2x^2 - 2 \]
Rearranging the terms in standard polynomial form gives us:
\[ x^3y - 2x^2 + xy - 2 \]
So, filling in the blanks in your format:
- \(x^3y\): coefficient is 1 (so in the blank it’s just \(1\))
- \(-2x^2\): coefficient is -2
- \(xy\): coefficient is 1
- constant term: -2
Thus, the simplified expression is:
\[ 1, (x^3y) + -2, (x^2) + 1, (xy) + -2 \]
The final answer is: \[ x^3y - 2x^2 + xy - 2 \]
So, the coefficients you need to fill in the blanks are:
\[ 1, -2, 1, -2 \]
1 answer