( 4 a − b ) 2 − 2 a ( 8 a + b ) (4a−b) 2 −2a(8a+b).

To simplify the expression \((4a - b)^2 - 2a(8a + b)\), we'll go through it step by step. 1. **Expand \((4a - b)^2\)**: \[ (4a - b)^2 = (4a - b)(4a - b) = 16a^2 - 8ab + b^2 \] 2. **Distribute \(-2a(8a + b)\)**: \[ -2a(8a + b) = -16a^2 - 2ab \] 3. **Combine the results**: Now substitute the expansions back into the expression: \[ (16a^2 - 8ab + b^2) + (-16a^2 - 2ab) \] Combine like terms: \[ (16a^2 - 16a^2) + (-8ab - 2ab) + b^2 = 0 - 10ab + b^2 \] Thus, the simplified form of the expression \((4a - b)^2 - 2a(8a + b)\) is: \[ b^2 - 10ab \]