Factorise
` 3( 2x- y) ^(3) +9 ( 2x- y) ^(2)`

Answer

To factorise the expression \( 3(2x - y)^3 + 9(2x - y)^2 \), we can follow these steps:

### Step 1: Identify common factors
Observe that both terms in the expression \( 3(2x - y)^3 \) and \( 9(2x - y)^2 \) have a common factor of \( (2x - y)^2 \).

### Step 2: Factor out the common factor
We can factor out \( 3(2x - y)^2 \) from both terms:
\[ 3(2x - y)^3 + 9(2x - y)^2 = 3(2x - y)^2 \left( (2x - y) + 3 \right) \]

### Step 3: Simplify the expression inside the parentheses
Now, simplify the expression inside the parentheses:
\[ (2x - y) + 3 = 2x - y + 3 \]

### Step 4: Write the final factored form
Putting it all together, we have:
\[ 3(2x - y)^2 (2x - y + 3) \]

Thus, the factored form of the expression \( 3(2x - y)^3 + 9(2x - y)^2 \) is:
\[ 3(2x - y)^2 (2x - y + 3) \]