Subtract the following expressions by the horizontal method.
2x − 3y + 4z from 4x − 6y − z

Hint: In horizontal subtraction, the expressions are arranged in a row ( in a horizontal manner ) in brackets with a negative sign in between. The like terms are then grouped together for simplification.

Complete step-by-step answer:
The constant with variable x can be subtracted from the constant that has x variable as its product and not y or z and the same applies to the other respective variables ( y and z ) as well.
 Writing expressions in a row with a negative sign we get:
4x − 6y – z − ( 2x − 3y + 4z )
Opening brackets and simplifying:
= 4x − 6y – z − 2x + 3y − 4z { All the terms are like ( product of constant and variable ) }
= 4x − 2x − 6y + 3y – z − 4z
= 2x − 3y − 5z
Therefore, subtracting the expression 2x − 3y + 4z from 4x − 6y − z by the horizontal method we get 2x − 3y − 5z as a result.

Note: After opening the brackets, when the term in the bracket after the negative sign is open, the sign of each term gets changed ( positive terms become negative and the negative ones become positive ).This is because when the negative sign is multiplied with a positive sign gives a negative sign and with a negative sign gives a positive.