Factorise by grouping method :
`m(x-3y)^(2) + n(3y - x) + 5x - 15y`

Answer

To factorise the expression \( m(x - 3y)^2 + n(3y - x) + 5x - 15y \) using the grouping method, we can follow these steps:

### Step 1: Rewrite the expression
Start with the original expression:
\[ m(x - 3y)^2 + n(3y - x) + 5x - 15y \]
Notice that \( 3y - x \) can be rewritten as \( -(x - 3y) \). Therefore, we can rewrite the expression as:
\[ m(x - 3y)^2 - n(x - 3y) + 5x - 15y \]

### Step 2: Factor out common terms
Now, we can group the terms that contain \( (x - 3y) \):
\[ m(x - 3y)^2 - n(x - 3y) + 5(x - 3y) \]
This can be simplified to:
\[ m(x - 3y)^2 + (5 - n)(x - 3y) \]

### Step 3: Factor out \( (x - 3y) \)
Now we can factor out \( (x - 3y) \):
\[ (x - 3y)(m(x - 3y) + (5 - n)) \]

### Step 4: Write the final factorised form
Thus, the final factorised form of the expression is:
\[ (x - 3y)(m(x - 3y) + 5 - n) \]