Question

Question

Using the Commutative Property, prove that these algebraic expressions are equivalent. In 1–2 sentences, explain your result.

Expression 1: y⋅3x


Expression 2: 3xy

Answer 1

To prove that the expressions \( y \cdot 3x \) and \( 3xy \) are equivalent using the Commutative Property, we can rearrange the factors in Expression 1:

1. Start with Expression 1: \( y \cdot 3x \).
2. Apply the Commutative Property: \( y \cdot 3x = 3 \cdot x \cdot y \).
3. Rearranging gives us \( 3 \cdot y \cdot x \), which is the same as \( 3xy \).

Thus, both expressions are equivalent. This result demonstrates that the order in which we multiply numbers does not affect the product, confirming the Commutative Property of multiplication.

Answer 2

can you seperate them and then answer the questions

Answer 3

Sure! Let’s separate the proof for each expression and then discuss the result.

Step 1: Expression 1

Expression 1: \( y \cdot 3x \)

Using the Commutative Property, we can rearrange the factors within the multiplication:

\[ y \cdot 3x = 3 \cdot x \cdot y \]

Step 2: Expression 2

Expression 2: \( 3xy \)

This expression can also be rewritten as:

\[ 3 \cdot x \cdot y \]

Conclusion

Now we see that both rearranged forms give us:

\[ y \cdot 3x = 3xy \]

Explanation of the Result

Both expressions are equivalent as they yield the same mathematical value when evaluated. This demonstrates the Commutative Property of multiplication, which states that changing the order of the factors does not change the product.

Answer 4

for the explanation can you make it sound less formal

Answer 5

Sure! Here’s a more casual explanation:

Both expressions, \(y \cdot 3x\) and \(3xy\), end up being the same when you switch around the numbers. That’s because when you multiply, it doesn’t matter what order you do it in. So, whether you write it as \(y \cdot 3x\) or \(3xy\), you get the same result!