**Subtracting linear expressions worksheet :**

Here we are going to some practice questions on subtracting linear expressions.

(1) Subtract -6p - 8 from -3p - 6

(2) Subtract 3xy - 4 from xy + 12

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

(4) Subtract 9p - 5q from -10p + 6q

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

(6) If A = 8x - 3y + 9, B = - y - 9 and C = 4x - y - 9

find A + B - C.

**Question 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 :**

**Question 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

**Question 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

**Example 6 : **

If A = 8x - 3y + 9, B = - y - 9 and C = 4x - y - 9

find A + B - C.

**Solution :**

A + B - C = (8x - 3y + 9) + (- y - 9) - (4x - y - 9)

= 8x - 3y + 9 - y - 9 - 4x + y + 9

= 8x - 4x - 3y - y + y + 9 - 9 + 9

= 4x - 4y + y + 9

= 4x - 3y + 9

Hence the answer is 4x - 3y + 9.

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