D. 64 iven that the two expression \( (x+a)(x-15) \) and \( x^{2}+b x+75 \) are identical calculate the value ib.

To determine the value of \(b\), we can expand the first expression: \[ (x + a)(x - 15) = x^2 - 15x + ax - 15a = x^2 + (a - 15)x - 15a \] Now, we set this equal to the second expression: \[ x^2 + bx + 75 \] From the coefficients, we can establish the following equations: 1. \(b = a - 15\) 2. \(-15a = 75\) From the second equation, we get: \[ -15a = 75 \implies a = -5 \] Now substituting \(a = -5\) into the first equation gives: \[ b = -5 - 15 = -20 \] Thus, the value of \(b\) is \(-20\).