To multiply the binomials \((5 + 2i)(5 - 2i)\), we can use the formula for the difference of squares, which states that \((a + b)(a - b) = a^2 - b^2\).
In this case, let:
- \(a = 5\)
- \(b = 2i\)
Using the difference of squares, we can find:
\[ (5 + 2i)(5 - 2i) = 5^2 - (2i)^2 \]
Calculating each term:
- \(5^2 = 25\)
- \((2i)^2 = 4i^2\)
Since \(i^2 = -1\), we have:
\[ 4i^2 = 4(-1) = -4 \]
Now substituting this back into the expression:
\[ (5 + 2i)(5 - 2i) = 25 - (-4) = 25 + 4 = 29 \]
Thus, the result of multiplying the binomials \((5 + 2i)(5 - 2i)\) is:
\[ \boxed{29} \]