factor the expression completely: $3x^{2}-3$.

Explanation:

Step1: Factor out the GCF

First, factor out the greatest - common factor (GCF) of the terms in the expression. The GCF of $3x^{2}$ and $3$ is $3$. So, $3x^{2}-3 = 3(x^{2}-1)$.

Step2: Use the difference - of - squares formula

The expression $x^{2}-1$ is a difference of squares, since $x^{2}-1=x^{2}-1^{2}$. The difference - of - squares formula is $a^{2}-b^{2}=(a + b)(a - b)$. Here, $a = x$ and $b = 1$. So, $x^{2}-1=(x + 1)(x - 1)$.

Answer:

$3(x + 1)(x - 1)$