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What is the sum of $5 x – 8 y + 2 z, 3 z – 4 y – 2 x, 6 y – z – x, and 3 x – 2 x – 3 y$ ?

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3 x + 9 y + 4 z

3 x - 9 y - 4 z

3 x - 3 y + 4 z

3 x - 9 y + 4 z

answer is D.

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Detailed Solution

Given,

5 x – 8 y + 2 z, 3 z – 4 y – 2 x, 6 y – z – x and 3 x – 2 x – 3 y

Add each term of given expression,

⇒ (5 x − 8 y + 2 z) + (3 z − 4 y − 2 x) + (6 y − z − x) + (3 x − 2 x − 3 y)

⇒ 5 x − 8 y + 2 z + 3 z − 4 y − 2 x + 6 y − z − x + 3 x − 2 x − 3 y

Separate each term of x, y and z.

⇒ (5 x − 2 x − x + 3 x − 2 x) + (− 8 y − 4 y + 6 y − 3 y) + (2 z + 3 z − z)

Take x, y and z common. We get,

⇒ x (5 − 2 − 1 + 3 − 2) + y (− 8 − 4 + 6 − 3) + z (2 + 3 − 1)

⇒ x (3) + y (− 9) + z (4)

⇒ 3 x − 9 y + 4 z

Hence, the sum of

5 x − 8 y + 2 z, 3 z − 4 y − 2 x, 6 y − z − x

and

3 x − 2 x − 3 y

3 x − 9 y + 4 z

.
Therefore, option 4 is correct.

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