Use the Commutative Property of Addition to rewrite the algebraic expression: 4x2+8x.

Answer 1

The Commutative Property of Addition states that the order of adding numbers does not change the sum.

Using this property, we can rearrange the terms in the given expression \(4x^2 + 8x\). The expression can be rewritten as:

\[ 8x + 4x^2 \]

Both \(4x^2 + 8x\) and \(8x + 4x^2\) are equivalent due to the Commutative Property of Addition.

Answer 2

Use the Commutative Property of Addition to rewrite the algebraic expression: ab2+c3
.

Answer 3

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

The expression can be rewritten as:

\[ c^3 + ab^2 \]

Both forms, \( ab^2 + c^3 \) 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: a20⋅x3
.

Answer 5

The Commutative Property of Multiplication states that the order of multiplying numbers does not change the product.

Using this property, we can rearrange the terms in the expression \( a^{20} \cdot x^3 \).

The expression can be rewritten as:

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

Both forms, \( a^{20} \cdot x^3 \) 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.
(14)( )(2)=(7)( )(14)

Answer 7

To fill in the blanks using the Commutative Property, we can rearrange the factors in each expression while maintaining equality.

Let's start with the left side:

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

We need to find a term to put in the first blank on the left side such that it can be rearranged to match the right-hand side \((7)(_)(14)\).

Notice that \(14\) can be factored as \(7 \cdot 2\). Therefore, we can fill in the blanks with \(2\) and \(7\):

The left side becomes: \[ (14)(7)(2) = (7)(2)(14) \]

So we have:

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

However, the first blank on the left side can remain empty, as \( (7) \) can be rearranged in both expressions. Thus, we can fill in the blanks as follows:

The completed expression is:

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

Alternatively, one could structure it as:

\[ (14)(1)(2) = (7)(4)(14) \]

where \( 1 \) is implied, making the left side equal to \( 14 \), leading to truth. This work assures you can fill in various suitable combinations based on spacing conventions as well.

The eventual final fill-in would be options: \[ (14)(7)(2) = (7)(2)(14) \]

1. Fill in \( 7 \) in the blank of the first expression and \( 2 \) in the second blank.

You can also conclude with existing variables persisting according to direct multiplication.

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 of Addition, we can rearrange the terms.

The expressions are:

\[ 5 + _ + 1 + 7 = 4 + _ + 7 + 1 \]

Let's analyze the left-hand side:

We have \(5 + _ + 1 + 7\). Since we want to make it equal to \(4 + _ + 7 + 1\), we notice that the term \(4\) on the right-hand side can be used to replace \(5\) if we take an appropriate value in place of the blanks.

If we take \(5\) from the left-hand side and set \(4\) in the right-hand side, we will fill the first blank with \(4\).

Now, for the second blank in each expression:

• To maintain the expression's value, we also have \(1\) on the left-hand side, so on the right-hand side, we will use \(1\) to fill in the blank.

Thus, the filled expressions become:

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

So the complete filled-in expressions are:

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

In summary, the blanks can be filled with \(4\) and \(5\):

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

Answer 10

Which of the following correctly demonstrates the use of the Commutative Property of Multiplication?(1 point)
Responses

11(b+z)=11b+11z
11 left parenthesis b plus z right parenthesis equals 11 b plus 11 z

z11⋅2=z11+2
z superscript 11 baseline times 2 equals z superscript 11 baseline plus 2

2(b10+z11)=(b10+z11)⋅2
2 left parenthesis b superscript 10 baseline plus z superscript 11 baseline right parenthesis equals left parenthesis b superscript 10 baseline plus z superscript 11 baseline right parenthesis times 2

3(b10+4)=3(4+b10)3
3 left parenthesis b superscript 10 baseline plus 4 right parenthesis equals 3 left parenthesis 4 plus b superscript 10 baseline right parenthesis 3

Answer 11

To correctly demonstrate the use of the Commutative Property of Multiplication, the order of the factors in multiplication can be rearranged without changing the product.

Let's analyze the options provided:

1. \(11(b + z) = 11b + 11z\)
   This illustrates the Distributive Property, not the Commutative Property.

2. \(z^{11} \cdot 2 = z^{11} + 2\)
   This is incorrect. The left side shows multiplication, while the right side incorrectly states addition instead of multiplication.

3. \(2(b^{10} + z^{11}) = (b^{10} + z^{11}) \cdot 2\)
   This shows that multiplying by \(2\) can occur to either the left or the right of the expression. It correctly demonstrates the Commutative Property of Multiplication for the factor \(2\).

4. \(3(b^{10} + 4) = 3(4 + b^{10})\)
   This shows the Commutative Property, but it is framed within the context of addition, not multiplication. It demonstrates that the order of addition can be swapped inside the parenthesis, but specifically it doesn't focus on the multiplication aspect.

Based on the analysis, the correct demonstration of the Commutative Property of Multiplication is:

\(2(b^{10} + z^{11}) = (b^{10} + z^{11}) \cdot 2\)

This option clearly shows that \(2\) can be multiplied either to the left or right of the sum inside the parentheses.