What is the product of the polynomials (x2y+2)(x2−y)?(1 point)
Responses
x4y−xy+x2y
x4y−x2y2+2x2−2y
x3y−x2y2+2x2−2y
x4y+x2−2y
The correct answer is x4y − xy + x2y.
To find the product of the polynomials (x^2y+2)(x^2−y), you can use the FOIL method, which stands for First, Outer, Inner, Last. Here's how you can do it step by step:
1. Multiply the first terms of each polynomial: (x^2y)(x^2) = x^4y.
2. Multiply the outer terms: (x^2y)(-y) = -x^2y^2.
3. Multiply the inner terms: (2)(x^2) = 2x^2.
4. Multiply the last terms: (2)(-y) = -2y.
Putting it all together, the product of the polynomials (x^2y+2)(x^2−y) is x^4y - x^2y^2 + 2x^2 - 2y.
So the correct answer is x^4y - x^2y^2 + 2x^2 - 2y.