We are asked to expand the product of two binomials, $(8 - 3a^2)(2a^2 + 6)$, and write the answer as a polynomial in standard form. Standard form means arranging the terms in decreasing order of exponents.

1. Problem Description

We are asked to expand the product of two binomials, $(8 - 3a^2)(2a^2 + 6)$, and write the answer as a polynomial in standard form. Standard form means arranging the terms in decreasing order of exponents.

2. Solution Steps

First, we multiply each term in the first binomial by each term in the second binomial using the distributive property (also known as FOIL):

$(8 - 3a^2)(2a^2 + 6) = 8(2a^2) + 8(6) - 3a^2(2a^2) - 3a^2(6)$

Next, we simplify each term:

$8(2a^2) = 16a^2$

$8(6) = 48$

$-3a^2(2a^2) = -6a^4$

$-3a^2(6) = -18a^2$

Now, we combine these terms:

$16a^2 + 48 - 6a^4 - 18a^2$

Combine like terms:

$(16a^2 - 18a^2) + 48 - 6a^4 = -2a^2 + 48 - 6a^4$

Finally, we write the polynomial in standard form (decreasing order of exponents):

$-6a^4 - 2a^2 + 48$

3. Final Answer

$-6a^4 - 2a^2 + 48$