Factorise:
`36x ^(3) y - 60x ^(2) y ^(3) z`

Answer

To factorise the expression \( 36x^3y - 60x^2y^3z \), we will follow these steps:

### Step 1: Identify the common factors
First, we need to find the greatest common factor (GCF) of the coefficients (36 and 60) and the variables in the expression.

- The coefficients are 36 and 60. The GCF of 36 and 60 is 12.
- For the variable \( x \), the lowest power is \( x^2 \) (since we have \( x^3 \) and \( x^2 \)).
- For the variable \( y \), the lowest power is \( y \) (since we have \( y \) and \( y^3 \)).

### Step 2: Write the common factor
Now we can write the common factor:
\[ \text{Common factor} = 12x^2y \]

### Step 3: Factor out the common factor
Next, we will factor out \( 12x^2y \) from the expression:
\[ 36x^3y - 60x^2y^3z = 12x^2y(3x - 5y^2z) \]

### Step 4: Write the final factored form
Thus, the final factored form of the expression is:
\[ 12x^2y(3x - 5y^2z) \]

### Summary of the solution
The expression \( 36x^3y - 60x^2y^3z \) can be factored as:
\[ 12x^2y(3x - 5y^2z) \]

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