Add the following expressions using both the horizontal method and column method:
$2 x - 5 y + 6 z$ and $- 3 x + 2 y - 7 z$

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Solution

Step 1: Adding the algebraic expressions by the horizontal method
Horizontal method: Taking care of signs, write all expressions in a horizontal line and group like terms together. Now, add these like terms and get the required sum.
We have $2 x - 5 y + 6 z$ and $- 3 x + 2 y - 7 z$
Now,
$(2 x - 5 y + 6 z) + (- 3 x + 2 y - 7 z) = 2 x - 5 y + 6 z - 3 x + 2 y - 7 z = 2 x - 3 x - 5 y + 2 y + 6 z - 7 z = (2 - 3) x + (- 5 + 2) y + (6 - 7) z = - 1 x + (- 3 y) + (- 1 z) = - x - 3 y - z$
Step 2: Adding the algebraic expressions by the column method
Column method: Write each expression in separate lines such that their like terms lie in the same vertical column. Taking care of signs, add each column.
$2 x - 5 y + 6 z + - 3 x + 2 y - 7 z_- x - 3 y - z__$
Hence, the required sum is $- x - 3 y - z$

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