Respuesta :
Option D: [tex](6x-1)(x-1)[/tex] is the product of the expression
Explanation:
The expression is [tex]6(x^{2} -1)\times\frac{6x-1}{6(x+1)}[/tex]
We need to determine the product of the expression.
To determine the product of the expression, we need to simplify the given expression.
Thus, we have,
[tex]6(x^{2} -1^2)\times\frac{6x-1}{6(x+1)}[/tex]
The term [tex](x^{2} -1^2)[/tex] is of the form [tex]a^2-b^2[/tex]
Now, we shall use the identity, [tex]a^2-b^2=(a+b)(a-b)[/tex]
Hence, we have,
[tex]6(x+1)(x-1)\times\frac{6(x-1)}{6(x+1)}[/tex]
Multiplying the terms and cancelling the common terms, we get,
[tex](x-1)\times({6x-1})[/tex]
Hence, the product of the given expression is [tex](6x-1)(x-1)[/tex]
Therefore, Option D is the correct answer.
