Question

factor the expression.
16d² + 25 =

Explanation:

Step1: Recognize sum of squares

$16d^2 = (4d)^2$, $25 = 5^2$

Step2: Check for real factorization

Sum of squares $a^2+b^2$ does not factor over real numbers. For complex numbers, use $a^2+b^2=(a+bi)(a-bi)$.

Step3: Apply complex factorization

Substitute $a=4d$, $b=5$:
$(4d+5i)(4d-5i)$

Answer:

$(4d + 5i)(4d - 5i)$ (or note that it is irreducible over the real numbers)