Question

preform the multiplication
(7x^2+a^2)(x^2-3a^2)

Answer 1

To perform the multiplication of the expression \((7x^2 + a^2)(x^2 - 3a^2)\), we will use the distributive property (also known as the FOIL method for binomials).

We multiply each term in the first bracket by each term in the second bracket:

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

1. Multiply \(7x^2\) by \(x^2\):

\[
7x^2 \cdot x^2 = 7x^4
\]

2. Multiply \(7x^2\) by \(-3a^2\):

\[
7x^2 \cdot -3a^2 = -21x^2 a^2
\]

3. Multiply \(a^2\) by \(x^2\):

\[
a^2 \cdot x^2 = a^2 x^2
\]

4. Multiply \(a^2\) by \(-3a^2\):

\[
a^2 \cdot -3a^2 = -3a^4
\]

Now, we combine all the results:

\[
7x^4 - 21x^2 a^2 + a^2 x^2 - 3a^4
\]

Next, we can combine similar terms (\(-21x^2a^2\) and \(a^2x^2\)):

\[
7x^4 + (-21 + 1)x^2 a^2 - 3a^4
\]

This simplifies to:

\[
7x^4 - 20x^2 a^2 - 3a^4
\]

So, the final result of multiplying \((7x^2 + a^2)(x^2 - 3a^2)\) is:

\[
\boxed{7x^4 - 20x^2 a^2 - 3a^4}
\]