multiply binomials

1. Identify the expression: The problem asks us to find the product of two binomials: $(3x^2 - 4)(x^2 - 5)$.

2. Apply the FOIL method: To multiply two binomials, we use the FOIL method (First, Outer, Inner, Last) to distribute each term in the first binomial to each term in the second binomial:
- First: Multiply the first terms: $(3x^2) \cdot (x^2) = 3x^4$
- Outer: Multiply the outer terms: $(3x^2) \cdot (-5) = -15x^2$
- Inner: Multiply the inner terms: $(-4) \cdot (x^2) = -4x^2$
- Last: Multiply the last terms: $(-4) \cdot (-5) = 20$

3. Combine the terms: Now, write out the sum of these products:
$$3x^4 - 15x^2 - 4x^2 + 20$$

4. Simplify by combining like terms: Identify the terms with the same power of $x$. Here, $-15x^2$ and $-4x^2$ are like terms:
$$-15x^2 - 4x^2 = -19x^2$$
So, the expression becomes:
$$3x^4 - 19x^2 + 20$$