Questions: Perform the indicated operation simplify. Express the answer (12-i)^2=

Solution Steps

To solve \((12 - i)^2\), we can use the formula for the square of a binomial: \((a - b)^2 = a^2 - 2ab + b^2\). Here, \(a = 12\) and \(b = i\). We will then simplify the expression by calculating each term and combining them.

To solve \((12 - i)^2\), we use the formula for the square of a binomial: \[ (a - b)^2 = a^2 - 2ab + b^2 \] Here, \(a = 12\) and \(b = i\).

Calculate each term separately: \[ a^2 = 12^2 = 144 \] \[ -2ab = -2 \cdot 12 \cdot i = -24i \] \[ b^2 = i^2 = -1 \]

Combine the calculated terms: \[ (12 - i)^2 = 144 - 24i + (-1) = 144 - 24i - 1 \] \[ = 143 - 24i \]

Final Answer