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Addition and Subtraction of Algebraic Expression

Subtract 2x...

Question

Subtract $2 x - 3 y + 4 z$ from $4 x - 6 y - z$ .

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Solution

$4 x - 6 y - z - (2 x - 3 y + 4 z) = 4 x - 6 y - z - 2 x + 3 y - 4 z$
$= (4 x - 2 x) + (- 6 y + 3 y) + (- z - 4 z)$
$= (2 x) + (- 3 y) + (- 5 z)$
$= 2 x - 3 y - 5 z$

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Similar questions

(2 x - 4 y + 3 z)

from the sum of

(x + 3 y - 4 z), (2 x + y - z)

(- 2 x + 3 y - z)

p_{1}, p_{2}, p_{3}

denote the distances of the plane 2x - 3y + 4z + 2 = 0 from the planes 2x - 3y + 4z + 6 = 0, 4x - 6y + 8z + 3 = 0 and 2x - 3y + 4z - 6 = 0 respectively, then

P_{1}, P_{2}, P_{3}

denotes the perpendicular distances of the plane

2 x - 3 y + 4 z + 2 = 0

from the parallel planes

2 x - 3 y + 4 z + 6 = 0, 4 x - 6 y + 8 z + 3 = 0

2 x - 3 y + 4 z - 6 = 0

respectively, then

p_{1}, p_{2}, p_{3}

denote the distance of the plane

2 x - 3 y + 4 z + 2 = 0

from the planes

2 x - 3 y + 4 z + 6 = 0, 4 x - 6 y + 8 z + 3 = 0

2 x - 3 y + 4 z - 6 = 0

respectively, then

Q. Distance between the two planes :

2 x + 3 y + 4 z = 4

4 x + 6 y + 8 z = 12

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