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(a) 7x+3y and -4x-2y
(b) 3a-2b+c+3 and a+3b-2c-4

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Solution

$\begin{matrix} (a) 7 x + 3 y a n d - 4 x - 2 y = (7 x + 3 y) + (- 4 x - 2 y) = 7 x + 3 y - 4 x - 2 y = 3 x + y (b) 3 a - 2 b + c + 3 a n d a + 3 b - 2 c - 4 = (3 a - 2 b + c + 3) + (a + 3 b - 2 c - 4) = 3 a - 2 b + c + 3 + a + 3 b - 2 c - 4 = 4 a + b - c - 1 \end{matrix}$

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∣ ∣ ∣ ∣ \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}

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∣ ∣ ∣ ∣ \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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