Use the Commutative Property of Addition to rewrite the algebraic expression: 4x^2+8x

The Commutative Property of Addition states that the order in which two numbers are added does not affect the sum. Therefore, to rewrite the expression \(4x^2 + 8x\) using the Commutative Property, you can simply rearrange the terms.

So, \(4x^2 + 8x\) can be rewritten as:

\[
8x + 4x^2
\]

Both forms represent the same expression.

Use the Commutative Property of Addition to rewrite the algebraic expression: ab^2+c^3

.(1 point)

Using the Commutative Property of Addition, which states that the order of addition does not affect the sum, you can rearrange the terms in the expression \( ab^2 + c^3 \).

So, the rewritten expression can be:

\[
c^3 + ab^2
\]

Both forms represent the same expression.

Use the Commutative Property of Multiplication to rewrite the algebraic expression: a^20⋅x^3

.(1 point)

The Commutative Property of Multiplication states that the order in which two numbers are multiplied does not affect the product.

Using this property, you can rewrite the expression \( a^{20} \cdot x^{3} \) by switching the order of the factors:

\[
x^3 \cdot a^{20}
\]

Both forms represent the same product.

Using the Commutative Property, fill in the blanks so that the two algebraic expressions are equivalent.(1 point)

(14)(__)(2)=(7)(__)(14)

To make the two expressions \( 14 \cdot (\_\_) \cdot 2 \) and \( 7 \cdot (\_\_) \cdot 14 \) equivalent using the Commutative Property, we can find the appropriate value for the blanks.

We can rewrite \( 7 \) in terms of \( 14 \) because \( 14 = 2 \cdot 7 \).

Thus, we can fill in the blanks using \( 1 \) for both blanks:

\[
(14) \cdot (1) \cdot (2) = (7) \cdot (2) \cdot (14)
\]

So the filled expressions would be:

\[
(14)(1)(2) = (7)(2)(14)
\]

Both sides equal \( 28 \).

(14)(__)(2)=(7)(2)(14)

fill in the blank

To fill in the blank so that the two expressions \( 14 \cdot (\_\_) \cdot 2 = 7 \cdot 2 \cdot 14 \) are equivalent, we can start simplifying the right side.

First, let's calculate the right side:

\[
7 \cdot 2 \cdot 14 = 14 \cdot 2 \cdot 7
\]
which simply rearranges using the Commutative Property.

Now, we want the left side to equal the right side. We can express \( 7 \) in terms of multiplication:

Notice that:
\[
7 = \frac{14}{2}
\]

So we can fill in the blank with \( \frac{14}{2} \) or just \( 7 \).

Thus, the complete expression is:

\[
(14)(7)(2) = (7)(2)(14)
\]

In summary, you can fill in the blank with **7**.

Thanks!!

You're welcome! If you have any more questions or need further assistance, feel free to ask. Happy studying!