Write $(3a + 4b + 5c)^2$ in expanded form.
Write $(3a + 4b + 5c)^2$ in expanded form.
Comparing the given expression with $(x+y+z)^{2}$, we find that
$x=3 a,\, y=4 b$ and $z=5 c$.
Therefore, using Identity $V$, we have
$(3 a+4 b+5 c)^{2} =(3 a)^{2}+(4 b)^{2}+(5 c)^{2}+2(3 a)(4 b)+2(4 b)(5 c)+2(5 c)(3 a)$
$=9 a^{2}+16 b^{2}+25 c^{2}+24 a b+40 b c+30 a c$
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