Question

Find the product of (3x2−8)(4x2+7)
. Provide your answer in descending order of exponents.(1 point)
(3x2−8)(4x2+7)=

Remaining Attempts : 3

Answer 1

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

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

\[
(3x^2)(4x^2) + (3x^2)(7) + (-8)(4x^2) + (-8)(7)
\]

Now let's compute each term:

1. \(3x^2 \cdot 4x^2 = 12x^4\)
2. \(3x^2 \cdot 7 = 21x^2\)
3. \(-8 \cdot 4x^2 = -32x^2\)
4. \(-8 \cdot 7 = -56\)

Now, we can combine like terms:

- The \(x^2\) terms: \(21x^2 - 32x^2 = -11x^2\)

Now, let's write the full expression, gathering everything together:

\[
(3x^2 - 8)(4x^2 + 7) = 12x^4 - 11x^2 - 56
\]

Putting it in descending order of exponents:

\[
12x^4 - 11x^2 - 56
\]

Thus, the final answer is:

\[
\boxed{12x^4 - 11x^2 - 56}
\]