Subtract $(2 a - 3 b + 4 c)$ from the sum of $(a + 3 b - 4 c), (4 a - b + 9 c)$ and $(- 2 b + 3 c - a)$ .

3 a + 2 b + 4 c

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2 a - 2 b + 4 c

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3 a - 4 b - 2 c

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2 a + 3 b + 4 c

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Solution

The correct option is D $2 a + 3 b + 4 c$
It is instructed to subtract $(2 a - 3 b + 4 c)$ from the sum of $(a + 3 b - 4 c), (4 a - b + 9 c)$ and $(- 2 b + 3 c - a)$ .

So, First we will do the sum of the three given polynomials,
Sum $= (a + 3 b - 4 c) + (4 a - b + 9 c) + (- 2 b + 3 c - a)$
$= (a + 4 a - a) + (3 b - b - 2 b) + (- 4 c + 9 c + 3 c)$
$= 4 a + 8 c$
Now, we can perform the subtraction,
$∴$ Required difference
$= (4 a + 8 c) - (2 a - 3 b + 4 c)$
$= 4 a + 8 c - 2 a + 3 b - 4 c$
$= 2 a + 3 b + 4 c$

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