4x(2x-1)-(x-3)(x+3)

Let's simplify the expression step by step:

Given expression:
\[4x(2x - 1) - (x - 3)(x + 3)\]

Step 1: Expand both parts.

• Expand \(4x(2x - 1)\):
  \[4x \times 2x = 8x^2\]
  \[4x \times (-1) = -4x\]

So, \(4x(2x - 1) = 8x^2 - 4x\).

• Expand \((x - 3)(x + 3)\):
  Recognize this as a difference of squares:
  \[(x)^2 - (3)^2 = x^2 - 9\]

Step 2: Write the expression with expanded parts:

\[8x^2 - 4x - (x^2 - 9)\]

Step 3: Distribute the minus sign:

\[8x^2 - 4x - x^2 + 9\]

Step 4: Combine like terms:

\[ (8x^2 - x^2) - 4x + 9 = 7x^2 - 4x + 9\]

Final Answer:

\[\boxed{7x^2 - 4x + 9}\]