Find the product of (3x2−8)(4x2+7)

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

We will multiply each term in the first polynomial by each term in the second polynomial:

1. **Multiply the first terms:**
\[
3x^2 \cdot 4x^2 = 12x^4
\]

2. **Multiply the outer terms:**
\[
3x^2 \cdot 7 = 21x^2
\]

3. **Multiply the inner terms:**
\[
-8 \cdot 4x^2 = -32x^2
\]

4. **Multiply the last terms:**
\[
-8 \cdot 7 = -56
\]

Now, we combine all these products together:
\[
12x^4 + 21x^2 - 32x^2 - 56
\]

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

So the expression simplifies to:
\[
12x^4 - 11x^2 - 56
\]

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