Q54. - Algebra 1

Question

Which equation below illustrates the Commutative Property?

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

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

C $xyz=yxz$

D $x+0=x$

Step-by-Step Solution

Answer

The equation representing the Commutative property is $xyz=yxz$ or option C.

Step 1. Use the definition of the commutative property.

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

 $\begin{array}{l}a+b=b+a\mathrm{.........................}\left(1\right)\\ abc=cba=cab\mathrm{...................}\left(2\right)\end{array}$

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:

 $xyz=yxz$