Question
Multiply the polynominal expression (x^2 y + 2)(x^2 - y)
Answers
GPT-4o mini
To multiply the polynomial expression \((x^2 y + 2)(x^2 - y)\), we can use the distributive property (also known as the FOIL method for binomials).
We can distribute each term in the first polynomial by each term in the second polynomial:
1. \(x^2y \cdot x^2\)
2. \(x^2y \cdot (-y)\)
3. \(2 \cdot x^2\)
4. \(2 \cdot (-y)\)
Now we will compute each of these products:
1. \(x^2y \cdot x^2 = x^{4}y\)
2. \(x^2y \cdot (-y) = -x^2y^2\)
3. \(2 \cdot x^2 = 2x^2\)
4. \(2 \cdot (-y) = -2y\)
Now, we can combine all these results:
\[
x^{4}y - x^{2}y^{2} + 2x^{2} - 2y
\]
So, the final result of multiplying the polynomial expressions \((x^2 y + 2)(x^2 - y)\) is:
\[
x^{4}y - x^{2}y^{2} + 2x^{2} - 2y
\]
We can distribute each term in the first polynomial by each term in the second polynomial:
1. \(x^2y \cdot x^2\)
2. \(x^2y \cdot (-y)\)
3. \(2 \cdot x^2\)
4. \(2 \cdot (-y)\)
Now we will compute each of these products:
1. \(x^2y \cdot x^2 = x^{4}y\)
2. \(x^2y \cdot (-y) = -x^2y^2\)
3. \(2 \cdot x^2 = 2x^2\)
4. \(2 \cdot (-y) = -2y\)
Now, we can combine all these results:
\[
x^{4}y - x^{2}y^{2} + 2x^{2} - 2y
\]
So, the final result of multiplying the polynomial expressions \((x^2 y + 2)(x^2 - y)\) is:
\[
x^{4}y - x^{2}y^{2} + 2x^{2} - 2y
\]