Question

find the product.
(5 + i)(5 − i)(2 + 3i)
(5 + i)(5 − i)(2 + 3i) = \boxed{} (type your answer in the form a + bi.)

Explanation:

Step1: Multiply (5 + i)(5 - i)

Using the difference of squares formula \((a + b)(a - b)=a^2 - b^2\), where \(a = 5\) and \(b = i\).
So \((5 + i)(5 - i)=5^2 - i^2=25 - (- 1)=25 + 1 = 26\).

Step2: Multiply the result by (2 + 3i)

Now we have \(26(2 + 3i)\). Using the distributive property \(a(b + c)=ab+ac\), where \(a = 26\), \(b = 2\) and \(c = 3i\).
So \(26\times2+26\times3i = 52+78i\).

Answer:

\(52 + 78i\)