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Addition and Subtraction of Algebraic Expression

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Question

$\begin{matrix} Add: x (x + y); y (y + z) : z (z + x) Add : 3 m (1 - m - n) and 2 n (m - n - 1) Subtract: 2 x (x - 3 y + 4 z) from x (7 x - y + 9 z) Subtract: (a - b + c) - 2 (- a + b - c) from 5 (a + 2 b - c) \end{matrix}$

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Solution

(1) $x (x + y) + y (y + z) + z (z + x)$
$= x^{2} + x y + y^{2} + y z + z^{2} + x z$
$= x^{2} + y^{2} + z^{2} + x y + y z + z x$

(2) $3 m (1 - m - n) + 2 n (m - n - 1)$
$= 3 m - 3 m^{2} - 3 m n + 2 m n - 2 n^{2} - 2 n$
$= 3 m - 2 n - 3 m^{2} - 2 n^{2} - m n$

(3) $x (7 x - y + 9 z) - 2 x (x - 3 y + 4 z)$
$= 7 x^{2} - x y + 9 x z - 2 x^{2} + 6 x y - 8 x z$
$= 5 x^{2} + 5 x y + x z$

(4) $5 (a + 2 b + c) - [a - b + c - 2 (- a + b + c)]$
$= 5 a + 10 b - 5 c - [3 a - 3 b + 3 c]$
$= 2 a + 13 b - 8 c$

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