**How to subtract linear expressions :**

To subtract linear expressions, we follow two methods

(i) Horizontal method

(ii) Vertical method

**Horizontal method :**

**Step 1 :**

Write the given expressions in a line.Now the first step is like ( ) - ( )

**Step 2 :**

Distribute the negative sign.

**Step 3 :**

Combine the like terms according to their sign.

**Vertical method method :**

**Step 1 :**

Write the given expressions vertically one by one.

**Step 2 :**

Change the original sign of the second expression.After changing the signs, we should not consider their old signs.

**Step 3 :**

Based on the sign that we have now we have to combine the terms.

Let us see some example problems for better understanding.

**Example 1 : **

Subtract -6p - 8 from -3p - 6

**Solution :**

**Horizontal method : **

= (-6p - 8) - (-3p - 6)

= -6p - 8 + 3p + 6

= -6p + 3p - 8 + 6

= -3p - 2

**Vertical method :**

**Example 2 : **

Subtract 3xy - 4 from xy + 12

**Solution :**

**Horizontal method : **

= (xy + 12) - (3xy - 4)

Distributing the negative sign, we get

= xy + 12 - 3xy + 4

= xy - 3xy + 12 + 4

= -2xy + 16

**Example 3 : **

Subtract m(n - 3) from n(5 - m)

**Solution :**

**Horizontal method : **

= n(5 - m) - m(n - 3)

Distributing n and m, we get

= 5n - nm - mn + 3m

= 5n - 2nm + 3m

**Example 4 : **

Subtract 9p - 5q from -10p + 6q

**Solution :**

**Horizontal method : **

= -10p + 6q - (9p - 5q)

= -10p + 6q - 9p + 5q

= -10p - 9p + 6q + 5q

= -19p + 11q

**Example 5 : **

Subtract 2(p - q) from 3(5p - q + 3)

**Solution :**

**Horizontal method : **

= 3(5p - q + 3) - 2(p - q)

= 15p - 3q + 9 - 2p + 2q

Combining the like terms

= 15p - 2p - 3q + 2q + 9

= 13p - q + 9

After having gone through the stuff given above, we hope that the students would have understood "How to subtract linear expressions".

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