Question

expand the polynomial.
(-10p^4+9)(9-10p^4)

Answer 1

To expand the polynomial \((-10p^4 + 9)(9 - 10p^4)\), we can use the distributive property (also known as the FOIL method for binomials). We will distribute each term in the first polynomial to each term in the second polynomial:

\[
(-10p^4)(9) + (-10p^4)(-10p^4) + (9)(9) + (9)(-10p^4)
\]

Now, we calculate each term:

1. \((-10p^4)(9) = -90p^4\)
2. \((-10p^4)(-10p^4) = 100p^8\)
3. \((9)(9) = 81\)
4. \((9)(-10p^4) = -90p^4\)

Next, we combine these results:

\[
100p^8 - 90p^4 - 90p^4 + 81
\]

Combine the like terms:

\(-90p^4 - 90p^4 = -180p^4\)

So, the expanded polynomial is:

\[
100p^8 - 180p^4 + 81
\]

Thus, the final result is:

\[
\boxed{100p^8 - 180p^4 + 81}
\]