Chapter 4 - Quadratic Functions and Equations - 4-8 Complex Numbers - Practice and Problem-Solving Exercises - Page 253: 33

$(x+5i)(x-5i)$

The given expression is equivalent to $x^2+5^2$. Recall: $a^2+b^2=(a+bi)(a-bi)$ Use the formula above with $a=x$ and $b=5$ to obtain: $x^2+25=x^2+5^2=(x+5i)(x-5i)$ Checking: \begin{align*} (x+5i)(x-5i)&=x^2-5xi+5xi-25i^2\\ &=x^2-25i^2\\ &=x^2-25(-1)\\ &=x^2+25 \end{align*}