**Add subtract and multiply linear expressions worksheet :**

You can find some practice questions on add, subtract and multiply linear expressions.

(1) Add 6a + 3 and 4a - 2

(2) Add 5y + 8 + 3z and 4y - 5

(3) Subtract 6a - 3b from - 8a + 9b

(4) Subtract a² + b² - 3ab from a² + b² - 3ab

(5) Multiply (3a - 2b) (2p + 3q)

(6) Multiply (3x - 7) (7x - 3)

**Question 1 :**

Add 6a + 3 and 4a - 2.

**Solution :**

**Adding linear expressions in horizontal method :**

** = (6a + 3) + (4a - 2)**

** = 6a + 4a + 3 - 2**

** = 10a + 1**

**Adding linear expressions in vertical method :**

**Question 2 :**

Add 5y + 8 + 3z and 4y - 5

**Solution : **

**Adding linear expressions in horizontal method :**

** = (**5y + 8 + 3z) + (4y - 5)

** = **5y + 4y + 8 - 5 + 3z

** = 9**y + 3z + 3

**Adding linear expressions in vertical method :**

**Question 4 :**

Subtract 6a - 3b from - 8a + 9b.

**Solution : **

**Subtracting linear expressions in horizontal method: **

** = (**- 8a + 9b) - (6a - 3b)

Distribute the negative sign inside the parentheses

** = **- 8a + 9b - 6a + 3b

= -8a - 6a + 9b + 3b

= -14a + 12b

**Subtracting linear expressions in vertical method :**

**Question 4 :**

Subtract a² + b² - 3ab from a² + b² - 3ab

**Solution : **

**Subtracting linear expressions in horizontal method: **

= (a² - b² - 3ab) - (a²+ b² - 3ab)

= a² - b² - 3ab - a² - b² + 3ab

= a² - a² - b² - b² - 3ab + 3ab

= - b² - b²

= - 2b²

**Subtracting linear expressions in vertical method :**

**Question 5 :**

Multiply (3a - 2b) (2p + 3q)

**Solution : **

By using distributive property we can multiply two polynomials.

= (3a - 2b) (2p + 3q)

= 3a(2p + 3q) - 2b(2p + 3q)

= 6ap + 9aq - 4pb - 6qb

Since there is not like terms, we cannot combine any more.

Hence the answer is 6ap + 9aq - 4pb - 6qb.

**Question 6 :**

Multiply (3x - 7) (7x - 3)

**Solution : **

By using distributive property we can multiply two polynomials.

= (3x - 7) (7x - 3)

= 3x(7x - 3) - 7(7x - 3)

= 21x² - 9x - 49x + 21

= 21x² - 58x + 21

Hence the answer is 21x² - 58x + 21.

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