Question

${\left(\frac{x}{2}+y+\frac{z}{3}\right)}^3+{\left(\frac{x}{3}-\frac{2y}{3}+z\right)}^3+{\left(-\frac{5x}{6}-\frac{y}{3}\frac{4z}{3}\right)}^3$

Answer 1

The given expression to be factorized is

Let, and. Then the given expression becomes

Note that

Recall the formula

When, this becomes

So, we have the new formula

, when.

Using the above formula, the given expression can be written as

Put, and.

Then we have

We cannot further factorize the expression.

So, the required factorization is of is