To simplify the expression \((5-a)(5+a)(25+a)\) and then square the result, we will first expand the product of the three terms:
\((5-a)(5+a)(25+a) = (25 - a^2)(25 + a) = 625 + 25a - 25a - a^2 • a = 625 - a^3\)
Now, to square the result, we will square the expression \((625 - a^3)\):
\((625 - a^3)^2 = 625^2 - 2 • 625 • a^3 + a^6\)
Finally, we simplify the expression further:
\(625^2 = 390625\)
\(-2 • 625 • a^3 = -1250a^3\)
\(a^6 = a^6\)
Therefore, the final result after squaring the given expression is:
\(390625 - 1250a^3 + a^6\)
