Distributive property of multiplication over addition is a very useful property that lets us simplify expressions in which we are multiplying a number by the sum of two or more other numbers.
The property states that the product of a number and the sum of two or more other numbers is equal to the sum 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) = 84
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 + z2)
Answer :
Use distributive property.
5(x2 + y2 + z2) = 5x2 + 5y2 + 5z2
Question 5 :
Evaluate using distributive property :
m(m2 + m + 5)
Answer :
Use distributive property.
m(m2 + m + 5) = m ⋅ m2 + m ⋅ m + 5m
m(m2 + m + 5) = m3 + m2 + 5m
Question 6 :
Write the given verbal phrase into algebraic expression
"3 times the sum of two different numbers"
Answer :
Let x and y be the two different numbers.
Then, 3 times the sum of two different numbers is
= 3(x + y)
Use distributive property.
= 3x + 3y
Question 7 :
If 4 times the sum 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
Subtract 20 from each side.
4x = 12
Divide each side by 4.
x = 3
So, the number is 3.
Question 8 :
If 7 times the sum of 3 times of a number and 6 is 147, find the number.
Answer :
Let x be the number.
Then,
7(3x + 6) = 147
Use distributive property.
21x + 42 = 147
Subtract 42 from each side.
21x = 105
Divide each side by 21.
x = 5
So, the number is 5.
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