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