**Using distributive property to simplify expressions worksheet :**

Worksheet on using distributive property to simplify expressions is much useful to the students who are at the initial stage of learning Algebra.

1. Simplify the expression given below.

5 - 3(7x + 8)

2. Simplify the expression given below.

-9a - (1/3)(-3/4 -2a/3 + 12)

3. Simplify the expression given below.

(2a - 3b + c) - 2(4b - 3a + c)

4. Simplify the expression given below.

14 + 5(x + 3) - 7x + 2

**Example 1 : **

Simplify the expression given below.

5 - 3(7x + 8)

**Solution : **

**Step 1 : **

Use the Distributive Property.

5 - 21x - 24

**Step 2 : **

Rewrite subtraction as adding the opposite.

5 + (-21x) + (-24)

**Step 3 :**

Use the Commutative Property.

5 + (-24) + (-21x)

**Step 4 :**

Combine like terms.

- 19 - 21x

Hence, 5 - 3(7x + 8) = - 19 - 21x

**Example 2 : **

Simplify the expression given below.

-9a - (1/3)(-3/4 -2a/3 + 12)

**Solution : **

**Step 1 : **

Use the Distributive Property.

-9a + 1/4 + 2a/9 - 4

**Step 2 :**

Rewrite subtraction as adding the opposite.

-9a + 1/4 + 2a/9 + (-4)

**Step 3 :**

Use the Commutative Property.

-9a + 2a/9 + 1/4 + (-4)

**Step 4 :**

Combine like terms.

- 79a/9 - 15/4

Hence, -9a + 1/4 + 2a/9 - 4 = - 79a/9 - 15/4

**Example 3 : **

Simplify the expression given below.

(2a - 3b + c) - 2(4b - 3a + c)

**Solution : **

**Step 1 : **

Use the Distributive Property.

2a - 3b + c - 8b + 6a - 2c

**Step 2 : **

Group the like terms

(2a + 6a) + (-3b - 8b) + (c - 2c)

**Step 3 :**

Simplify

8a - 11b - c

Hence, (2a - 3b + c) - 2(4b - 3a + c) = 8a - 11b - c

**Example 4 : **

Simplify the expression given below.

14 + 5(x + 3) - 7x + 2

**Solution : **

**Step 1 : **

Use the Distributive Property.

14x + 5x + 15 - 7x + 2

**Step 2 : **

Group the like terms

(14x + 5x - 7x) + (15 + 2)

**Step 3 :**

Simplify

11x + 17

Hence, 14 + 5(x + 3) - 7x = 11x + 17

After having gone through the stuff given above, we hope that the students would have understood "Using distributive property to simplify expressions worksheet".

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