To determine which expression is equivalent to [tex]\(2 (x^2 - 1) + 3 x (x - 4)\)[/tex], we need to simplify the given expression.
First, we expand each part of the given expression:
1. Simplify [tex]\(2 (x^2 - 1)\)[/tex]:
[tex]\[
2 (x^2 - 1) = 2 \cdot x^2 - 2 \cdot 1 = 2x^2 - 2
\][/tex]
2. Simplify [tex]\(3 x (x - 4)\)[/tex]:
[tex]\[
3 x (x - 4) = 3x \cdot x - 3x \cdot 4 = 3x^2 - 12x
\][/tex]
Next, we combine the simplified results from steps 1 and 2:
[tex]\[
2x^2 - 2 + 3x^2 - 12x
\][/tex]
Combine like terms:
[tex]\[
(2x^2 + 3x^2) + (-12x) + (-2) = 5x^2 - 12x - 2
\][/tex]
Hence, the expression [tex]\(2 (x^2 - 1) + 3 x (x - 4)\)[/tex] simplifies to [tex]\(5x^2 - 12x - 2\)[/tex].
So, the correct match is:
4) [tex]\(5 x^2 - 12 x - 2\)[/tex]
