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Addition and Subtraction of Algebraic Expression

Subtract: 3x...

Question

Subtract:
$3 x (x - y - z) + 3 y (x - y + z) + 3 z (x + y - z)$ from $3 (x + y) (x - y) + 3 z (2 y + z)$

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Solution

To find: $3 x (x - y - z) + 3 y (x - y + z) + 3 z (x + y - z) - (3 (x + y) (x - y) + 3 z (2 y + z))$
$= 3 x^{2} - 3 x y - 3 x z + 3 x y - 3 y^{2} + 3 y z + 3 z x + 3 y z - 3 z^{2} - (3 x^{2} - 3 y^{2} + 6 y z + 3 z^{2})$
$= 3 x^{2} - 3 x^{2} - 3 x y + 3 x y - 3 x z + 3 x z - 3 y^{2} + 3 y^{2} + 3 y z + 3 y z - 6 y z - 3 z^{2} - 3 z^{2}$
$= - 6 z^{2}$

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