Fractorise:
`x ^(3) (2a -b) + x^(2) (2a -b)`

Answer

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

### Step 1: Identify the common factor
In the given expression, both terms \( x^3(2a - b) \) and \( x^2(2a - b) \) share a common factor of \( (2a - b) \).

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

### Step 3: Factor the remaining expression
Now, we need to factor the expression \( x^3 + x^2 \). Here, we can see that \( x^2 \) is a common factor:
\[ x^3 + x^2 = x^2(x + 1) \]

### Step 4: Combine the factors
Now we can combine the factors we found:
\[ (2a - b)(x^2(x + 1)) \]

### Final Answer
Thus, the fully factorised form of the expression \( x^3(2a - b) + x^2(2a - b) \) is:
\[ (2a - b)x^2(x + 1) \]

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