Write the expanded form of $(9a + 8b + 2c)^2$

Solution:

Use identity:
$(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$

Here:
$a = 9a,; b = 8b,; c = 2c$

Now expand:

$(9a)^2 = 81a^2$
$(8b)^2 = 64b^2$
$(2c)^2 = 4c^2$

$2(9a \cdot 8b) = 144ab$
$2(8b \cdot 2c) = 32bc$
$2(9a \cdot 2c) = 36ac$

Final Answer:

$81a^2 + 64b^2 + 4c^2 + 144ab + 32bc + 36ac$