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

Answer 1

The Commutative Property of Addition states that the order in which you add numbers does not change the sum. Thus, to rewrite the expression \(4x^2 + 8x\) using this property, you can rearrange the terms.

One possible rearrangement of the expression is:

\[ 8x + 4x^2 \]

Both expressions \(4x^2 + 8x\) and \(8x + 4x^2\) are equivalent, demonstrating the commutative property.

Answer 2

next one is
ab^2+c^3

Answer 3

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

One possible rearrangement is:

\[ c^3 + ab^2 \]

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

Answer 4

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

Answer 5

To fill in the blanks using the Commutative Property of Addition, we want both sides of the equation to be equal while ensuring that the order of the terms may change.

Given the expression:

\[ (14) + ___ \cdot (2) = (7) + ___ \cdot (14) \]

We can use the same term on both sides of the equation:

A suitable value to fill in the blanks is \(x\), where:

For the left side:
\( (14) + (x) \cdot (2) \)

For the right side:
\( (7) + (x) \cdot (14) \)

After substituting for \(x\):

Let's choose \(x = 1\) to simplify:

So we get:

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

This translates to:

\[ 14 + 2 = 7 + 14 \]

This does not balance out.

To correctly fill the blanks, let's use another approach:

If we want both sides to balance out perfectly, we must have:

For the left side we can express as multiples:

Let’s choose \(x = 7\)

Then it shows:

\[ (14) + (0) \cdot (2) = (7) + (7) \cdot (14) \]

However using constants doesn’t yield properly.

To ensure balance can we use:

Making it \(14\) corresponding to double:

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

In the structure of \(abounds\) we must ensure of similar dispatch rulings.

Finally settle numbers to \(x = 0\)

Thus:

Then completed equation results -

Final answer decline - still need referencing.

Answer 6

so its (14)(x)(2) = (7)(z)(14)

Answer 7

It looks like you're aiming to find appropriate values for \(x\) and \(z\) in the equation:

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

To find suitable values for \(x\) and \(z\) that make both sides of the equation equal, we can simplify both sides first:

1. Left side: \((14)(x)(2) = 28x\)

2. Right side: \((7)(z)(14) = 98z\)

Now we need these two expressions to be equal:

\[ 28x = 98z \]

To isolate \(z\), we can divide both sides by 28:

\[ x = \frac{98z}{28} \]

This simplifies to:

\[ x = 3.5z \]

This means for any value of \(z\), you can find the corresponding value of \(x\).

Example Choices

• If you choose \(z = 1\): \[ x = 3.5 \times 1 = 3.5 \]

• If you choose \(z = 2\): \[ x = 3.5 \times 2 = 7 \]

So, you can choose values based on your needs. Just ensure that you keep the relation \(x = 3.5z\) to maintain equivalence.