Factorise:
`8x ^(2) -72xy + 12x`

Answer

To factorise the expression \( 8x^2 - 72xy + 12x \), we will follow these steps:

### Step 1: Identify the common factor
Look for the greatest common factor (GCF) in all the terms of the expression. The terms are \( 8x^2 \), \( -72xy \), and \( 12x \). The GCF of the coefficients \( 8, -72, \) and \( 12 \) is \( 4 \), and the variable \( x \) is present in all terms.

### Step 2: Factor out the GCF
Now, we will factor out \( 4x \) from the expression:
\[ 8x^2 - 72xy + 12x = 4x(2x - 18y + 3) \]

### Step 3: Simplify the expression inside the parentheses
The expression inside the parentheses is \( 2x - 18y + 3 \). We can rearrange it for clarity, but it cannot be simplified further.

### Final Factored Form
Thus, the final factored form of the expression is:
\[ 4x(2x - 18y + 3) \]