Add the following expressions using column method:
$2 a + 3 b - 9, 4 a - 6 b, 3 a + 2 b, 6 a - 2 b$

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Solution

Here each expression is written in a separate row such that the like terms are arranged one below the other. Then the addition of terms is carried out:
$2 a + 3 b - 9 4 a - 6 b 3 a + 2 b 6 a - 2 b 15 a - 3 a - 9$

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Add the following expressions using column method:

$5 a - 6 b, 7 a + 8 b, - 5 a + 2 b$

∣ ∣ ∣ ∣ \begin{matrix} a & a + b & a + b + c 2 a & 3 a + 2 b & 4 a + 3 b + 2 c 3 a & 6 a + 3 b & 10 a + 6 b + 3 a \end{matrix} ∣ ∣ ∣ ∣ = a^{3}

∣ ∣ ∣ ∣ \begin{matrix} a & a + b & a + b + c 2 a & 3 a + 2 b & 4 a + 3 b + 2 c 3 a & 6 a + 3 b & 10 a + 6 b + 3 c \end{matrix} ∣ ∣ ∣ ∣ = a^{3}

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