Solving the Equation (x+12)(x12) = 481
This equation involves a product of two binomials, which can be easily expanded using the difference of squares pattern: (a + b)(a  b) = a²  b²

Expand the equation: (x + 12)(x  12) = 481 becomes x²  144 = 481

Rearrange the equation: x²  144  481 = 0 x²  625 = 0

Factor the equation: This is a difference of squares pattern again! (x + 25)(x  25) = 0

Solve for x: For the product of two factors to equal zero, at least one of the factors must be zero. Therefore:
 x + 25 = 0 => x = 25
 x  25 = 0 => x = 25
Therefore, the solutions to the equation (x + 12)(x  12) = 481 are x = 25 and x = 25.