The equivalent expression of x ( y + z ) by using the commutative property.

Question

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Answer 1

Question

Chapter DPT, Problem 1E

(A)

To determine

To find: The equivalent expression of $x(y+z)$ by using the commutative property.

(A)

Expert Solution

Answer to Problem 1E

The expression $x(y+z)$ is equivalent to $(y+z)x$ .

Explanation of Solution

Given:

The expression is $x(y+z)$ .

Property used:

Commutative property:

“The order of factors does not affect the result of expression”.

That is, if x commutes with y under the operation $"⋅"$ , then $x⋅y=y⋅x$ .

Illustration:

The factors of the given expression $x(y+z)$ are $x$ and $(y+z)$ .

Apply the commutative property by changing the order of factors to obtain the required equivalent expression.

That is, $x(y+z)$ is altered to $(y+z)x$ .

Therefore, the expression $x(y+z)$ is equivalent to $(y+z)x$ .

(B)

To determine

To find: The equivalent expression of $2+(x+y)$ by using the associative property.

(B)

Expert Solution

Answer to Problem 1E

The expression $2+(x+y)$ is equivalent to $(2+x)+y$ .

Explanation of Solution

Given:

The expression is $2+(x+y)$ .

Property used:

Associative property:

The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.

That is, the property of associative under “ $+$ ” operation states that $(a+b)+c=a+(b+c)$ .

Illustration:

Apply the associative property by changing the group of terms to obtain the required equivalent expression.

That is, $2+(x+y)$ is altered to $(2+x)+y$ .

Therefore, the expression of $2+(x+y)$ is equivalent to $(2+x)+y$ .

(C)

To determine

To find: The equivalent expression of $(2+3)x$ by using the distributive property.

(C)

Expert Solution

Answer to Problem 1E

The expression $(2+3)x$ is equivalent to $2x+3x$ .

Explanation of Solution

Given:

The expression is $(2+3)x$ .

Property used:

Distributive property:

The property of left distributive under multiplication over addition state that $(a+b)c=ac+bc$ .

Illustration:

Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.

That is, $(2+3)x$ is altered to $2x+3x$ .

Hence, the expression of $(2+3)x$ equivalent to $2x+3x$ .

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Answer 2

Question

Chapter DPT, Problem 1E

(A)

To determine

To find: The equivalent expression of $x(y+z)$ by using the commutative property.

(A)

Expert Solution

Answer to Problem 1E

The expression $x(y+z)$ is equivalent to $(y+z)x$ .

Explanation of Solution

Given:

The expression is $x(y+z)$ .

Property used:

Commutative property:

“The order of factors does not affect the result of expression”.

That is, if x commutes with y under the operation $"⋅"$ , then $x⋅y=y⋅x$ .

Illustration:

The factors of the given expression $x(y+z)$ are $x$ and $(y+z)$ .

Apply the commutative property by changing the order of factors to obtain the required equivalent expression.

That is, $x(y+z)$ is altered to $(y+z)x$ .

Therefore, the expression $x(y+z)$ is equivalent to $(y+z)x$ .

(B)

To determine

To find: The equivalent expression of $2+(x+y)$ by using the associative property.

(B)

Expert Solution

Answer to Problem 1E

The expression $2+(x+y)$ is equivalent to $(2+x)+y$ .

Explanation of Solution

Given:

The expression is $2+(x+y)$ .

Property used:

Associative property:

The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.

That is, the property of associative under “ $+$ ” operation states that $(a+b)+c=a+(b+c)$ .

Illustration:

Apply the associative property by changing the group of terms to obtain the required equivalent expression.

That is, $2+(x+y)$ is altered to $(2+x)+y$ .

Therefore, the expression of $2+(x+y)$ is equivalent to $(2+x)+y$ .

(C)

To determine

To find: The equivalent expression of $(2+3)x$ by using the distributive property.

(C)

Expert Solution

Answer to Problem 1E

The expression $(2+3)x$ is equivalent to $2x+3x$ .

Explanation of Solution

Given:

The expression is $(2+3)x$ .

Property used:

Distributive property:

The property of left distributive under multiplication over addition state that $(a+b)c=ac+bc$ .

Illustration:

Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.

That is, $(2+3)x$ is altered to $2x+3x$ .

Hence, the expression of $(2+3)x$ equivalent to $2x+3x$ .

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Answer 3

Question

Chapter DPT, Problem 1E

(A)

To determine

To find: The equivalent expression of $x(y+z)$ by using the commutative property.

(A)

Expert Solution

Answer to Problem 1E

The expression $x(y+z)$ is equivalent to $(y+z)x$ .

Explanation of Solution

Given:

The expression is $x(y+z)$ .

Property used:

Commutative property:

“The order of factors does not affect the result of expression”.

That is, if x commutes with y under the operation $"⋅"$ , then $x⋅y=y⋅x$ .

Illustration:

The factors of the given expression $x(y+z)$ are $x$ and $(y+z)$ .

Apply the commutative property by changing the order of factors to obtain the required equivalent expression.

That is, $x(y+z)$ is altered to $(y+z)x$ .

Therefore, the expression $x(y+z)$ is equivalent to $(y+z)x$ .

(B)

To determine

To find: The equivalent expression of $2+(x+y)$ by using the associative property.

(B)

Expert Solution

Answer to Problem 1E

The expression $2+(x+y)$ is equivalent to $(2+x)+y$ .

Explanation of Solution

Given:

The expression is $2+(x+y)$ .

Property used:

Associative property:

The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.

That is, the property of associative under “ $+$ ” operation states that $(a+b)+c=a+(b+c)$ .

Illustration:

Apply the associative property by changing the group of terms to obtain the required equivalent expression.

That is, $2+(x+y)$ is altered to $(2+x)+y$ .

Therefore, the expression of $2+(x+y)$ is equivalent to $(2+x)+y$ .

(C)

To determine

To find: The equivalent expression of $(2+3)x$ by using the distributive property.

(C)

Expert Solution

Answer to Problem 1E

The expression $(2+3)x$ is equivalent to $2x+3x$ .

Explanation of Solution

Given:

The expression is $(2+3)x$ .

Property used:

Distributive property:

The property of left distributive under multiplication over addition state that $(a+b)c=ac+bc$ .

Illustration:

Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.

That is, $(2+3)x$ is altered to $2x+3x$ .

Hence, the expression of $(2+3)x$ equivalent to $2x+3x$ .

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Answer 4

Question

Chapter DPT, Problem 1E

(A)

To determine

To find: The equivalent expression of $x(y+z)$ by using the commutative property.

(A)

Expert Solution

Answer to Problem 1E

The expression $x(y+z)$ is equivalent to $(y+z)x$ .

Explanation of Solution

Given:

The expression is $x(y+z)$ .

Property used:

Commutative property:

“The order of factors does not affect the result of expression”.

That is, if x commutes with y under the operation $"⋅"$ , then $x⋅y=y⋅x$ .

Illustration:

The factors of the given expression $x(y+z)$ are $x$ and $(y+z)$ .

Apply the commutative property by changing the order of factors to obtain the required equivalent expression.

That is, $x(y+z)$ is altered to $(y+z)x$ .

Therefore, the expression $x(y+z)$ is equivalent to $(y+z)x$ .

(B)

To determine

To find: The equivalent expression of $2+(x+y)$ by using the associative property.

(B)

Expert Solution

Answer to Problem 1E

The expression $2+(x+y)$ is equivalent to $(2+x)+y$ .

Explanation of Solution

Given:

The expression is $2+(x+y)$ .

Property used:

Associative property:

The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.

That is, the property of associative under “ $+$ ” operation states that $(a+b)+c=a+(b+c)$ .

Illustration:

Apply the associative property by changing the group of terms to obtain the required equivalent expression.

That is, $2+(x+y)$ is altered to $(2+x)+y$ .

Therefore, the expression of $2+(x+y)$ is equivalent to $(2+x)+y$ .

(C)

To determine

To find: The equivalent expression of $(2+3)x$ by using the distributive property.

(C)

Expert Solution

Answer to Problem 1E

The expression $(2+3)x$ is equivalent to $2x+3x$ .

Explanation of Solution

Given:

The expression is $(2+3)x$ .

Property used:

Distributive property:

The property of left distributive under multiplication over addition state that $(a+b)c=ac+bc$ .

Illustration:

Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.

That is, $(2+3)x$ is altered to $2x+3x$ .

Hence, the expression of $(2+3)x$ equivalent to $2x+3x$ .

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Answer 5

Chapter DPT, Problem 1E

(A)

To determine

To find: The equivalent expression of $x(y+z)$ by using the commutative property.

(A)

Expert Solution

Answer to Problem 1E

The expression $x(y+z)$ is equivalent to $(y+z)x$ .

Explanation of Solution

Given:

The expression is $x(y+z)$ .

Property used:

Commutative property:

“The order of factors does not affect the result of expression”.

That is, if x commutes with y under the operation $"⋅"$ , then $x⋅y=y⋅x$ .

Illustration:

The factors of the given expression $x(y+z)$ are $x$ and $(y+z)$ .

Apply the commutative property by changing the order of factors to obtain the required equivalent expression.

That is, $x(y+z)$ is altered to $(y+z)x$ .

Therefore, the expression $x(y+z)$ is equivalent to $(y+z)x$ .

(B)

To determine

To find: The equivalent expression of $2+(x+y)$ by using the associative property.

(B)

Expert Solution

Answer to Problem 1E

The expression $2+(x+y)$ is equivalent to $(2+x)+y$ .

Explanation of Solution

Given:

The expression is $2+(x+y)$ .

Property used:

Associative property:

The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.

That is, the property of associative under “ $+$ ” operation states that $(a+b)+c=a+(b+c)$ .

Illustration:

Apply the associative property by changing the group of terms to obtain the required equivalent expression.

That is, $2+(x+y)$ is altered to $(2+x)+y$ .

Therefore, the expression of $2+(x+y)$ is equivalent to $(2+x)+y$ .

(C)

To determine

To find: The equivalent expression of $(2+3)x$ by using the distributive property.

(C)

Expert Solution

Answer to Problem 1E

The expression $(2+3)x$ is equivalent to $2x+3x$ .

Explanation of Solution

Given:

The expression is $(2+3)x$ .

Property used:

Distributive property:

The property of left distributive under multiplication over addition state that $(a+b)c=ac+bc$ .

Illustration:

Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.

That is, $(2+3)x$ is altered to $2x+3x$ .

Hence, the expression of $(2+3)x$ equivalent to $2x+3x$ .

Answer 6

Chapter DPT, Problem 1E

(A)

To determine

To find: The equivalent expression of $x(y+z)$ by using the commutative property.

(A)

Expert Solution

Answer to Problem 1E

The expression $x(y+z)$ is equivalent to $(y+z)x$ .

Explanation of Solution

Given:

The expression is $x(y+z)$ .

Property used:

Commutative property:

“The order of factors does not affect the result of expression”.

That is, if x commutes with y under the operation $"⋅"$ , then $x⋅y=y⋅x$ .

Illustration:

The factors of the given expression $x(y+z)$ are $x$ and $(y+z)$ .

Apply the commutative property by changing the order of factors to obtain the required equivalent expression.

That is, $x(y+z)$ is altered to $(y+z)x$ .

Therefore, the expression $x(y+z)$ is equivalent to $(y+z)x$ .

Answer 7

Chapter DPT, Problem 1E

(A)

To determine

To find: The equivalent expression of $x(y+z)$ by using the commutative property.

Answer 8

(A)

Expert Solution

Answer to Problem 1E

The expression $x(y+z)$ is equivalent to $(y+z)x$ .

Answer 9

(A)

Expert Solution

Answer 10

(A)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

The expression is $x(y+z)$ .

Property used:

Commutative property:

“The order of factors does not affect the result of expression”.

That is, if x commutes with y under the operation $"⋅"$ , then $x⋅y=y⋅x$ .

Illustration:

The factors of the given expression $x(y+z)$ are $x$ and $(y+z)$ .

Apply the commutative property by changing the order of factors to obtain the required equivalent expression.

That is, $x(y+z)$ is altered to $(y+z)x$ .

Therefore, the expression $x(y+z)$ is equivalent to $(y+z)x$ .

Answer 13

(B)

To determine

To find: The equivalent expression of $2+(x+y)$ by using the associative property.

(B)

Expert Solution

Answer to Problem 1E

The expression $2+(x+y)$ is equivalent to $(2+x)+y$ .

Explanation of Solution

Given:

The expression is $2+(x+y)$ .

Property used:

Associative property:

The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.

That is, the property of associative under “ $+$ ” operation states that $(a+b)+c=a+(b+c)$ .

Illustration:

Apply the associative property by changing the group of terms to obtain the required equivalent expression.

That is, $2+(x+y)$ is altered to $(2+x)+y$ .

Therefore, the expression of $2+(x+y)$ is equivalent to $(2+x)+y$ .

Answer 14

(B)

To determine

To find: The equivalent expression of $2+(x+y)$ by using the associative property.

Answer 15

(B)

Expert Solution

Answer to Problem 1E

The expression $2+(x+y)$ is equivalent to $(2+x)+y$ .

Answer 16

(B)

Expert Solution

Answer 17

(B)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

The expression is $2+(x+y)$ .

Property used:

Associative property:

The grouping of any two numbers in an expression which contains more than two terms does affect the resulting expression.

That is, the property of associative under “ $+$ ” operation states that $(a+b)+c=a+(b+c)$ .

Illustration:

Apply the associative property by changing the group of terms to obtain the required equivalent expression.

That is, $2+(x+y)$ is altered to $(2+x)+y$ .

Therefore, the expression of $2+(x+y)$ is equivalent to $(2+x)+y$ .

Answer 20

(C)

To determine

To find: The equivalent expression of $(2+3)x$ by using the distributive property.

(C)

Expert Solution

Answer to Problem 1E

The expression $(2+3)x$ is equivalent to $2x+3x$ .

Explanation of Solution

Given:

The expression is $(2+3)x$ .

Property used:

Distributive property:

The property of left distributive under multiplication over addition state that $(a+b)c=ac+bc$ .

Illustration:

Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.

That is, $(2+3)x$ is altered to $2x+3x$ .

Hence, the expression of $(2+3)x$ equivalent to $2x+3x$ .

Answer 21

(C)

To determine

To find: The equivalent expression of $(2+3)x$ by using the distributive property.

Answer 22

(C)

Expert Solution

Answer to Problem 1E

The expression $(2+3)x$ is equivalent to $2x+3x$ .

Answer 23

(C)

Expert Solution

Answer 24

(C)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given:

The expression is $(2+3)x$ .

Property used:

Distributive property:

The property of left distributive under multiplication over addition state that $(a+b)c=ac+bc$ .

Illustration:

Apply the left distributive property under multiplication over addition to obtain the required equivalent expression.

That is, $(2+3)x$ is altered to $2x+3x$ .

Hence, the expression of $(2+3)x$ equivalent to $2x+3x$ .

Answer 27

The equivalent expression of x ( y + z ) by using the commutative property.

Concept explainers

Videos

To find: The equivalent expression of $x(y+z)$ by using the commutative property.

Answer to Problem 1E

Explanation of Solution

To find: The equivalent expression of $2+(x+y)$ by using the associative property.

Answer to Problem 1E

Explanation of Solution

To find: The equivalent expression of $(2+3)x$ by using the distributive property.

Answer to Problem 1E

Explanation of Solution

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Chapter DPT Solutions

The equivalent expression of x ( y + z ) by using the commutative property.

Concept explainers

Videos

To find: The equivalent expression of x(y+z)<m:math><m:mrow><m:mi>x</m:mi><m:mrow><m:mo>(</m:mo><m:mrow><m:mi>y</m:mi><m:mo>+</m:mo><m:mi>z</m:mi></m:mrow><m:mo>)</m:mo></m:mrow></m:mrow></m:math> by using the commutative property.

Answer to Problem 1E

Explanation of Solution

To find: The equivalent expression of 2+(x+y)<m:math><m:mrow><m:mn>2</m:mn><m:mo>+</m:mo><m:mrow><m:mo>(</m:mo><m:mrow><m:mi>x</m:mi><m:mo>+</m:mo><m:mi>y</m:mi></m:mrow><m:mo>)</m:mo></m:mrow></m:mrow></m:math> by using the associative property.

Answer to Problem 1E

Explanation of Solution

To find: The equivalent expression of (2+3)x<m:math><m:mrow><m:mrow><m:mo>(</m:mo><m:mrow><m:mn>2</m:mn><m:mo>+</m:mo><m:mn>3</m:mn></m:mrow><m:mo>)</m:mo></m:mrow><m:mi>x</m:mi></m:mrow></m:math> by using the distributive property.

Answer to Problem 1E

Explanation of Solution

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Chapter DPT Solutions

To find: The equivalent expression of $x(y+z)$ by using the commutative property.

To find: The equivalent expression of $2+(x+y)$ by using the associative property.

To find: The equivalent expression of $(2+3)x$ by using the distributive property.