Subtract the sum of 5x − 4y + 6z and −8x + y − 2z from the sum of 12x − y + 3z and −3x + 5y − 8z.

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Solution

Add 5x − 4y + 6z and −8x + y − 2z.

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

Adding 12x − y + 3z and −3x + 5y − 8z:
(12x − y + 3z )+(−3x + 5y − 8z)
= 12x − y + 3z −3x + 5y − 8z
= (12-3)x +(−1+5)y + (3-8)z
= 9x +4y -5z

Subtract -3x − 3y + 4z from 9x +4y -5z.
Change the sign of each term of the expression that is to be subtracted and then add.

Term to be subtracted = -3x − 3y + 4z
Changing the sign of each term of the expression gives 3x + 3y - 4z.
On adding:
(9x +4y -5z)+(3x + 3y - 4z )
= 9x +4y -5z+3x + 3y - 4z
= (9+3)x +(4+3)y + (-5-4)z
= 12x +7y -9z

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