Using the commutative property, prove that these algebraic expressions are equivalent
Y•3x
3xy
To prove that the algebraic expressions Y•3x and 3xy are equivalent using the commutative property, we need to show that the order of their terms can be switched without changing the result.
The commutative property states that the order of terms can be changed without affecting the result.
For the expression Y•3x, the order is Y and then 3x. If we switch the order of these terms using the commutative property, we have 3x•Y.
For the expression 3xy, the order is 3x and then y. If we switch the order of these terms using the commutative property, we have y•3x.
Since both Y•3x and 3xy can be rearranged to 3x•Y and y•3x respectively, we can conclude that the expressions are equivalent based on the commutative property.
To prove that the algebraic expressions Y•3x and 3xy are equivalent using the commutative property, we need to show that the order of multiplication does not affect the result.
The commutative property states that for any two numbers a and b, the order of the operation does not change the result. In other words, a • b = b • a.
Now let's apply the commutative property to the given expressions:
Y•3x = 3x•Y
By rearranging the order of multiplication, we can see that Y•3x is equivalent to 3x•Y.
Therefore, we have proved using the commutative property that the algebraic expressions Y•3x and 3xy are equivalent.
To prove that the expressions Y•3x and 3xy are equivalent using the commutative property, we need to show that they can be rearranged without changing their value.
According to the commutative property of multiplication, the order of multiplication does not affect the result. In other words, for any two numbers a and b, a•b = b•a.
Let's apply this property to the expressions:
Y•3x = 3x•Y
We rearranged the order of the terms Y and 3x without changing their value. Therefore, Y•3x and 3xy are equivalent expressions.