Factor the expression over the set of complex numbers $$25 a ^ { 2 } + 16$$
A) $\quad ( 5 a + 4 i ) ( 5 a - 4 i )$
B) $\quad ( 5 + 4 i ) ( 5 - 4 i )$
C) $\quad ( - 5 a + 4 i ) ( - 5 a + 4 i )$
D) $\quad ( 5 a + 4 i ) ( 5 a + 4 i )$
E) $\quad ( 5 a + 4 ) ( 5 a - 4 )$

Question

Quizplus · Accepted Answer

The expression can be written as the sum of squares $(5a)^2 + (4i)^2$. We can then use the difference of squares identity to factor as $(5a + 4i)(5a - 4i)$. Note that this factorization is unique and cannot be further simplified.

Factor the Expression Over the Set of Complex Numbers 25a2+1625 a ^ { 2 } + 1625a2+16

Factor the Expression Over the Set of Complex Numbers $25 a ^ { 2 } + 16$