3x to the power 3 - 12xy

The terms are $3x^3$ and $-12xy$.
The numerical coefficients are 3 and -12. The GCF of 3 and 12 is 3.
The variable parts are $x^3$ and $x$. The GCF of $x^3$ and $x$ is $x$.
The variable $y$ is only present in the second term, so it is not a common factor.
Therefore, the GCF of the entire expression is $3x$.

Divide each term by $3x$:

So, the expression becomes $3x(x^2 - 4y)$.

The term inside the parentheses, $x^2 - 4y$, cannot be factored further using standard algebraic identities (like difference of squares) because $4y$ is not a perfect square of a single term.

The completely factorised expression is $3x(x^2 - 4y)$.

3x(x^2 - 4y)