DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER SUBTRACTION

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, 

Practice Questions

Question 1 : 

Evaluate using distributive property :

7(10 - 2)

Answer :

Use distributive property.

7(10 - 2)  =  7(10) - 7(2)

7(10 - 2)  =  70 - 14 

7(10 - 2)  =  56

Question 2 : 

Evaluate using distributive property :

6(x - y)

Answer :

Use distributive property.

6(x - y)  =  6x - 6y

Question 3 : 

Evaluate using distributive property :

m(n - p)

Answer :

Use distributive property.

m(n - p)  =  mn - mp

Question 4 : 

Evaluate using distributive property :

5(x² - y²)

Answer :

Use distributive property.

5(x² - y²)  =  5x² - 5y²

Question 5 : 

Evaluate using distributive property :

m(m² - m)

Answer :

Use distributive property.

m(m² - m)  =  m ⋅ m² - m ⋅ m

m(m² - m)  =  m³ - m²

Question 6 : 

Write the given verbal phrase into algebraic expression

"3 times the difference of two different numbers"

Answer :

Let x and y be the two different numbers.

Then, 

3 times the difference of two different numbers is 

=  3(x - y)

Use distributive property.

=  3x - 3y

Question 7 : 

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

Answer :

Let x be the number. 

Then,

4(x - 5)  =  32

Use distributive property. 

4x - 20  =  32

Add 20 to each side. 

4x  =  52

Divide each side by 4.

x  =  13

So, the number is 13. 

Question 8 : 

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

Answer :

Let x be the number. 

Then,

7(3x - 6)  =  147

Use distributive property.

21x - 42  =  147

Add 42 to each side. 

21x  =  189

Divide each side by 21.

x  =  9

So, the number is 9. 

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