**Distributive property of multiplication over subtraction is a very useful property that lets us simplify ****expressions in which we are multiplying a number by the difference of two other numbers.**

**The property states that the product of a number and the difference of two other numbers is equal to the difference of the products.**

**More clearly, **

**Example 1 : **

Evaluate using distributive property : 7(10 - 2)

**Solution :**

7(10 - 2) = 7(10) - 7(2)

7(10 - 2) = 70 - 14

7(10 - 2) = **56**

**Example 2 : **

Evaluate using distributive property : 6(x - y)

**Solution :**

6(x - y) = **6x - 6y**

**Example 3 : **

Evaluate using distributive property : m(n - p)

**Solution :**

m(n - p) = **mn - mp**

**Example 4 : **

Evaluate using distributive property : 5(x² - y²)

**Solution :**

5(x² - y²) = **5x****²**** - 5y²**

**Example 5 : **

Evaluate using distributive property : m(m² - m)

**Solution :**

m(m² - m) = m.m² - m.m

m(m² - m) = **m****³ - m²**

**Problem 1 : **

Write the given verbal phrase into algebraic expression

**"3 times the difference of two different numbers"**

**Solution :**

Let "x" and "y" be the two different numbers.

Then,

The difference of two different numbers = x - y

3 times the sum of two different numbers = ** 3(x - y) **

**Problem 2 : **

If 4 times the difference of a number and 5 is 32, find the number.

**Solution :**

Let "x" be the required number.

According to the question, we have

4(x - 5) = 32

4x - 20 = 32

4x = 52

x = 13

**Hence the required number is 13.**

**Problem 3 : **

Write the given verbal phrase into algebraic expression

**"6 times 3 less than 4 times of a number"**

**Solution :**

Let "x" be the number.

Then,

4 times of number = 4x

3 less than 4 times of number = 4x - 3

6 times 3 less than 4 times of a number = 6(4x - 3)

6 times 3 less than 4 times of a number = ** 24x - 18**

**Problem 4 : **

If 7 times 6 less than 3 times of a number is 147, find the number.

**Solution :**

Let "x" be the required number.

According to the question, we have

7(3x - 6) = 147

21x - 42 = 147

21x = 189

x = 9

**Hence the required number is 9.**

**Problem 5 : **

If 9 times the difference of 7 and 4 times of a number is 27, find the number.

**Solution :**

Let "x" be the required number.

According to the question, we have

9(7 - 4x) = 27

63 - 36x = 27

36 = 36x

1 = x

**Hence the required number is 1.**

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