Question

Which of the following expression is equal to x^2+25?

Answer 1

The answer is (x-5i)(x+5i)

Answer 2

A: (x + 5i)^2
= (x + 5i)(x + 5i)
= (x)(x) + (x)(5i) + (5i)(x) + (5i)(5i)
= x^2 + 5ix + 5ix + 25i^2
= 25i^2 + 10ix + x^2


B: (x - 5i)^2
= (x  +   - 5i)(x +  - 5i)
= (x)(x) + (x)(- 5i) + (- 5i)(x) + (- 5i)(- 5i)
= x^2 - 5ix - 5ix + 25i^2
= 25i^2 - 10ix + x^2


C: (x - 5i)(x + 5i)
= (x +  - 5i)(x + 5i)
= (x)(x) + (x)(5i) + (- 5i)(x) + (- 5i)(5i)
= x^2 + 5ix - 5ix - 25i^2
= 25i^2 + x^2


D: (x + 10i)(x  - 15i)
= (x + 10i)(x +  - 15i)
= (x)(x) + (x)(- 15i) + (10i)(x) + (10i)(- 15i)
= x^2 - 15ix + 10ix - 150i^2
=  - 150i^2 + 5ix + x^2



Hope that helps!!!