3x to the power 3 - 12xy

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 $3x(x^2 - 4y)$.

$3x(x^2 - 4y)$

3x(x^2 - 4y)

3 done, 2 left today. You're making progress.