Write $(3a + 4b + 5c)^2$ in expanded form.

Comparing the given expression with $(x + y + z)^2$,we identify that $x = 3a$,$y = 4b$,and $z = 5c$.
Using the algebraic identity $(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx$,we substitute the values:
$(3a + 4b + 5c)^2 = (3a)^2 + (4b)^2 + (5c)^2 + 2(3a)(4b) + 2(4b)(5c) + 2(5c)(3a)$
Calculating each term:
$(3a)^2 = 9a^2$
$(4b)^2 = 16b^2$
$(5c)^2 = 25c^2$
$2(3a)(4b) = 24ab$
$2(4b)(5c) = 40bc$
$2(5c)(3a) = 30ac$
Thus,the expanded form is $9a^2 + 16b^2 + 25c^2 + 24ab + 40bc + 30ac$.