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

Question

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

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Answer

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 $(x+y+z)^2=x^2+y^2+z^2+2 x y+2 y z+2 z x$
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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