**Problem 1 : **

Evaluate using distributive property :

7(10 + 2)

**Problem 2 : **

Evaluate using distributive property :

6(x + y)

**Problem 3 : **

Evaluate using distributive property :

m(n + p)

**Problem 4 : **

Evaluate using distributive property :

5(x^{2} + y^{2} + z^{2})

**Problem 5 : **

Evaluate using distributive property :

m(m^{2} + m + 5)

**Problem 6 : **

Write the given verbal phrase into algebraic expression

"3 times the sum of two different numbers"

**Problem 7 : **

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

**Problem 8 : **

Write the given verbal phrase into algebraic expression :

"6 times the sum of three different numbers"

**Problem 9 : **

If 7 times the sum of 3 times of a number and 6 is 147, find the number.

**Problem 10 : **

If 9 times the sum of 7 and 4 times of a number is 135, find the number.

**Problem 1 : **

Evaluate using distributive property :

7(10 + 2)

**Solution :**

**Use distributive property.**

7(10 + 2) = 7(10) + 7(2)

7(10 + 2) = 70 + 14

7(10 + 2) = 84

**Problem 2 : **

Evaluate using distributive property :

6(x + y)

**Solution :**

**Use distributive property.**

6(x + y) = 6x + 6y

**Problem 3 : **

Evaluate using distributive property :

m(n + p)

**Solution :**

**Use distributive property.**

m(n + p) = mn + mp

**Problem 4 : **

Evaluate using distributive property :

5(x^{2} + y^{2} + z^{2})

**Solution :**

**Use distributive property.**

5(x^{2} + y^{2} + z^{2}) = 5x^{2} + 5y^{2} + 5z^{2}

**Problem 5 : **

Evaluate using distributive property :

m(m^{2} + m + 5)

**Solution :**

**Use distributive property.**

m(m^{2} + m + 5) = m ⋅ m^{2} + m ⋅ m + 5m

m(m^{2} + m + 5) = m^{3} + m^{2} + 5m

**Problem 6 : **

Write the given verbal phrase into algebraic expression

"3 times the sum of two different numbers"

**Solution :**

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

**Problem 7 : **

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

**Solution :**

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.

**Problem 8 : **

Write the given verbal phrase into algebraic expression :

"6 times the sum of three different numbers"

**Solution :**

Let x, y and z be the three different numbers.

Then, 6 times the um of three different numbers is

= 6(x + y + z)

Use distributive property.

= 6x + 6y + 6z

**Problem 9 : **

If 7 times the sum of 3 times of a number and 6 is 147, find the number.

**Solution :**

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.

**Problem 10 : **

If 9 times the sum of 7 and 4 times of a number is 135, find the number.

**Solution :**

Let x be the number.

Then,

9(7 + 4x) = 135

Use distributive property.

63 + 36x = 135

Subtract 63 from each side.

36x = 72

Divide each side by 36.

x = 2

So, the number is 2.

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