To factorise the expression $3x^3 - 12xy$ completely, we will find the greatest common factor. Step 1: Identify the greatest common factor (GCF). 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 $3x$. Step 2: Factor out the GCF. Divide each term by $3x$: $$ \frac{3x^3}{3x} = x^2 $$ $$ \frac{-12xy}{3x} = -4y $$ So, the expression becomes $3x(x^2 - 4y)$. Step 3: Check for further factorisation. 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 $3x(x^2 - 4y)$. $$3x(x^2 - 4y)$$ \boxed{3x(x^2 - 4y)} 3 done, 2 left today. You're making progress.