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

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Solution

Assume x = 3a + 4b.

Using algebraic identity, we can write

$(3 a + 4 b + 5 c)^{2}$ = $x^{2} + 25 c^{2} + 10 x c$

= $(3 a + 4 b)^{2}$ + $25 c^{2}$ + 10(3a + 4b)c

= $9 a^{2}$ + $16 b^{2}$ + 24ab + $25 c^{2}$ + 30ac + 40bc

= $9 a^{2}$ + $16 b^{2}$ + $25 c^{2}$ + 24ab + 30ac + 40bc

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