What is the factored form of the expression over the complex numbers? 4x^2+25y^2 (2x+5iy)(2x+5iy) (2x-5iy)(2x-5iy) (2x-5y)(2x+5y) (2x+5iy)(2x-5iy)

## Step 1The given expression is . We need to factorize this expression over the complex numbers.## Step 2The formula for the difference of squares is \(a^2 - b^2 = (a + b)(a - b)\). However, the given expression is a sum of squares, not a difference.## Step 3We can use the identity \(a^2 + b^2 = (a + bi)(a - bi)\) to factorize a sum of squares. Here, is the imaginary unit, and .## Step 4Substitute and into the identity. We get:### \((2x)^2 + (5y)^2 = (2x + 5yi)(2x - 5yi)\)