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Chapter 2: Q54. (page 117)

Which equation below illustrates the Commutative Property?

A (3x+4y)+2z=3x+(4y+2z)

B 7(x+y)=7x+7y

C xyz=yxz

Dx+0=x

Short Answer

Expert verified

The equation representing the Commutative property isxyz=yxz or option C.

Step by step solution

01

Step 1. Use the definition of the commutative property.

The commutative property is for addition and multiplication are given as shown:

a+b=b+a.........................1abc=cba=cab...................2

02

Step 2. Identify the expression having commutative property.

We are given the expressions:

A (3x+4y)+2z=3x+(4y+2z)

B 7(x+y)=7x+7y

C xyz=yxz

D x+0=x

Observe that in option A bracket is with the first two terms on the left-hand side and then on the right-hand side it is with the last two terms, we call such associations as associative property.

Similarly, option B is the distributive property

Option C is a commutative property by definition in step-1

Option D is an identity property.

Hence, the following equation represents the commutative property:

xyz=yxz

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