Question

what is the product?
$6\left(x^{2}-1\
ight)\cdot\frac{6x - 1}{6(x + 1)}$
\\(\circ\\) $6(x - 1)^{2}$
\\(\circ\\) $6(x^{2}-1)$
\\(\circ\\) $(x + 1)(6x - 1)$
\\(\circ\\) $(x - 1)(6x - 1)$

Explanation:

Step1: Factor the difference of squares

Recall that \(a^2 - b^2=(a + b)(a - b)\). So, \(x^2-1=(x + 1)(x - 1)\). The expression becomes \(6(x + 1)(x - 1)\cdot\frac{6x - 1}{6(x + 1)}\).

Step2: Cancel common factors

Cancel out the common factors \(6\) and \((x + 1)\) from the numerator and the denominator. After canceling, we are left with \((x - 1)(6x - 1)\).

Answer:

\((x - 1)(6x - 1)\) (corresponding to the option with this expression)