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

Question

.(1 point)

Answer 1

The Commutative Property of Addition states that changing the order of the addends does not change the sum. Therefore, you can rewrite the expression \(4x^2 + 8x\) in a different order.

Rewriting it, we can say:

\[ 8x + 4x^2 \]

Both forms are equivalent because of the Commutative Property of Addition.

Answer 2

Use the Commutative Property of Addition to rewrite the algebraic expression: ab^2 + c^3
.(1 point)

Answer 3

Using the Commutative Property of Addition, we can rearrange the expression \( ab^2 + c^3 \) in a different order.

One possible way to rewrite it is:

\[ c^3 + ab^2 \]

Both expressions \( ab^2 + c^3 \) and \( c^3 + ab^2 \) are equivalent due to the Commutative Property of Addition.

Answer 4

Use the Commutative Property of Multiplication to rewrite the algebraic expression: a^20 ⋅ x^3
.(1 point)

Answer 5

Using the Commutative Property of Multiplication, we can rearrange the expression \( a^{20} \cdot x^3 \) in a different order.

One possible way to rewrite it is:

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

Both expressions \( a^{20} \cdot x^3 \) and \( x^3 \cdot a^{20} \) are equivalent due to the Commutative Property of Multiplication.

Answer 6

Using the Commutative Property, fill in the blanks so that the two algebraic expressions are equivalent.(1 point)
(14)
(
)(2)=(7)
(
)(14)

Answer 7

To make the two expressions equivalent using the Commutative Property, we need to use the same factors in different orders.

The first expression is:

\[ 14 \cdot (_)(2) \]

The second expression is:

\[ 7 \cdot (_)(14) \]

Let's analyze the components:

1. We can start with the first expression. We can rewrite \( 14 \) as \( 7 \cdot 2 \). Thus: \[ 14 \cdot (7) \cdot (2) \] becomes: \[ (7 \cdot 2) \cdot (2) \]

2. The second expression is \( 7 \cdot (2) \cdot (14) \).

Now, if we fill in the blanks in the first equation while making sure the second expression is equivalent, we can use:

• First blank: \( 7 \)
• Second blank: \( 2 \)

So we can fill in the blanks like this:

(14) \((7)\)(2) = (7) \((2)\)(14)

Thus, the completed expression is: \[ 14 \cdot (7) \cdot (2) = 7 \cdot (2) \cdot (14) \]

Both sides are indeed equivalent due to the Commutative Property.

Answer 8

Using the Commutative Property, fill in the blanks so that the two algebraic expressions are equivalent.(1 point)
5+( )
+1+7=4+ ( )
+7+1

Answer 9

To make the two expressions equivalent using the Commutative Property, we want to fill in the blanks such that both sides have the same terms rearranged.

The left side of the equation is:

\[ 5 + ( _ ) + 1 + 7 \]

The right side of the equation is:

\[ 4 + ( _ ) + 7 + 1 \]

To make both expressions equivalent, we notice that both sides currently include the numbers \(5\), \(1\), and \(7\) on the left, and \(4\), \(7\), and \(1\) on the right.

We want to determine what to put in the blanks.

1. For the left side, if we find a number to replace the blank that will maintain the equality, we see that \(5\) can be rewritten using \(4\).

2. Therefore, let’s fill the blanks as follows:

   • First blank on the left side: \(4\)
   • Second blank on the right side: \(5\)

So our completed expression becomes:

\[ 5 + (4) + 1 + 7 = 4 + (5) + 7 + 1 \]

This equality holds, and rearranging the numbers in any order due to the Commutative Property of Addition maintains the equality.