factorise`x^(4)y-2x^(3)y^(2)`

Answer

To factorize the expression \( x^4y - 2x^3y^2 \), we can follow these steps:

### Step 1: Identify the common factors
We start by looking for common factors in both terms of the expression. The two terms are \( x^4y \) and \( -2x^3y^2 \).

### Step 2: Factor out the common terms
The common factors in both terms are:
- The variable \( x \): The lowest power of \( x \) in the terms is \( x^3 \).
- The variable \( y \): The lowest power of \( y \) in the terms is \( y \).

Thus, we can factor out \( x^3y \) from both terms.

### Step 3: Write the expression after factoring out the common terms
After factoring out \( x^3y \), we rewrite the expression:
\[ x^4y - 2x^3y^2 = x^3y(x - 2y) \]

### Final Factorized Form
The factorized form of the expression is:
\[ x^3y(x - 2y) \]