What is the product of the polynomials left parenthesis x squared plus 2 right parenthesis left parenthesis x squared minus y right parenthesis

Answer 1

To find the product of the polynomials \((x^2 + 2)(x^2 - y)\), we can use the distributive property (also known as the FOIL method for binomials):

\[ (x^2 + 2)(x^2 - y) = x^2(x^2) + x^2(-y) + 2(x^2) + 2(-y) \]

Now, we will calculate each term:

1. \(x^2 \cdot x^2 = x^4\)
2. \(x^2 \cdot (-y) = -yx^2\)
3. \(2 \cdot x^2 = 2x^2\)
4. \(2 \cdot (-y) = -2y\)

Now, we can combine these results:

\[ x^4 - y x^2 + 2 x^2 - 2 y \]

Next, we combine the like terms \( -yx^2 + 2x^2 \):

\[ x^4 + (2 - y)x^2 - 2y \]

So, the product of the polynomials \((x^2 + 2)(x^2 - y)\) is:

\[ \boxed{x^4 + (2 - y)x^2 - 2y} \]