https://file.aiquickdraw.com/mathbot/file/1727371493763rmfnt6ha.jpg

The expression shown in the image is \( x^2 + 16 \).

This is a sum of squares, which cannot be factored using real numbers. The sum of squares does not factor in the same way as a difference of squares, such as \( x^2 - 16 = (x - 4)(x + 4) \).

However, it can be factored using complex numbers:

\[
x^2 + 16 = (x - 4i)(x + 4i)
\]

Here, \( i \) is the imaginary unit, where \( i^2 = -1 \).

Would you like more details on how this factorization works or have any other questions?

Here are some related questions for you to explore:

1. How do you factor a difference of squares?
2. Can a sum of cubes be factored similarly?
3. What is the process of factoring polynomials with complex numbers?
4. How does the quadratic formula apply to complex roots?
5. What are the applications of imaginary numbers in solving equations?

**Tip**: When working with polynomials, always check if the form is a sum or difference of squares, as this determines how it can be factored!

Learn how to factor the expression x^2 + 16 using complex numbers. This detailed solution explores the sum of squares and introduces the concept of imaginary numbers, ideal for students in Grades 9-12.

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