Simplify the polynomial expression (xy - 2) (x^2 + 1)

Question

___x^3y + ___x^2 + ___ xy + ___
Fill in blanks

Answer 1

To simplify the polynomial expression \((xy - 2)(x^2 + 1)\), we will use the distributive property (also known as the FOIL method for binomials) to multiply the two expressions.

1. Distribute \(xy\) to both terms in \((x^2 + 1)\):

   • \(xy \cdot x^2 = x^3y\)
   • \(xy \cdot 1 = xy\)

2. Distribute \(-2\) to both terms in \((x^2 + 1)\):

   • \(-2 \cdot x^2 = -2x^2\)
   • \(-2 \cdot 1 = -2\)

Now, combine all the results together: \[ x^3y + xy - 2x^2 - 2 \]

This simplifies to: \[ x^3y - 2x^2 + xy - 2 \]

Now, let's fill in the blanks in your question: ___x^3y + ___x^2 + ___xy + ___

We have:

• The coefficient of \(x^3y\) is \(1\)
• The coefficient of \(x^2\) is \(-2\)
• The coefficient of \(xy\) is \(1\)
• The constant term is \(-2\)

Thus, we fill in the blanks as follows:

1. 1
2. -2
3. 1
4. -2

So, the final answer is: 1 (for \(x^3y\)), -2 (for \(x^2\)), 1 (for \(xy\)), -2 (for the constant).