The problem is to expand the given function $f(x)=(2x^4 - 3)(x^2 + 1)$.

1. Problem Description

The problem is to expand the given function $f(x)=(2x^4 - 3)(x^2 + 1)$.

2. Solution Steps

We need to expand the given expression by multiplying each term in the first parenthesis with each term in the second parenthesis.

$f(x) = (2x^4 - 3)(x^2 + 1)$

$f(x) = 2x^4(x^2 + 1) - 3(x^2 + 1)$

$f(x) = 2x^4(x^2) + 2x^4(1) - 3(x^2) - 3(1)$

Using the rule $x^a \cdot x^b = x^{a+b}$, we have:

$2x^4(x^2) = 2x^{4+2} = 2x^6$

Substituting this back into the equation:

$f(x) = 2x^6 + 2x^4 - 3x^2 - 3$

3. Final Answer

$f(x) = 2x^6 + 2x^4 - 3x^2 - 3$