Find the product of (3x2−8)(4x2+7)

To find the product of the expressions \( (3x^2 - 8)(4x^2 + 7) \), we can use the distributive property (also known as the FOIL method for binomials).

1. **Distribute \(3x^2\):**
\[
3x^2 \cdot 4x^2 = 12x^4
\]
\[
3x^2 \cdot 7 = 21x^2
\]

2. **Distribute \(-8\):**
\[
-8 \cdot 4x^2 = -32x^2
\]
\[
-8 \cdot 7 = -56
\]

Now, combine all these results together:
\[
(3x^2 - 8)(4x^2 + 7) = 12x^4 + 21x^2 - 32x^2 - 56
\]

Next, combine the like terms:
\[
21x^2 - 32x^2 = -11x^2
\]

Putting it all together, we get:
\[
12x^4 - 11x^2 - 56
\]

Thus, the final result in descending order of exponents is:
\[
\boxed{12x^4 - 11x^2 - 56}
\]