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,
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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