Use the distributive property to write an equivalent expression.

To use the distributive property on the expression \( 9(4f - 4g + 6) \), you need to multiply each term inside the parentheses by \( 9 \).

Here's how to do it:

1. Multiply \( 9 \) by \( 4f \):
\[
9 \times 4f = 36f
\]

2. Multiply \( 9 \) by \( -4g \):
\[
9 \times -4g = -36g
\]

3. Multiply \( 9 \) by \( 6 \):
\[
9 \times 6 = 54
\]

Now, combine all these results:
\[
9(4f - 4g + 6) = 36f - 36g + 54
\]

So the equivalent expression is:
\[
36f - 36g + 54
\]

Use the distributive property to write an equivalent expression.

2(r + 7)

To use the distributive property on the expression \( 2(r + 7) \), you need to multiply each term inside the parentheses by \( 2 \).

Here's how to do it:

1. Multiply \( 2 \) by \( r \):
\[
2 \times r = 2r
\]

2. Multiply \( 2 \) by \( 7 \):
\[
2 \times 7 = 14
\]

Now, combine these results:
\[
2(r + 7) = 2r + 14
\]

So, the equivalent expression is:
\[
2r + 14
\]

Use the distributive property to write an equivalent expression.

10(2p - 3q + 6)

To use the distributive property on the expression \( 10(2p - 3q + 6) \), you need to multiply each term inside the parentheses by \( 10 \).

Here are the steps:

1. Multiply \( 10 \) by \( 2p \):
\[
10 \times 2p = 20p
\]

2. Multiply \( 10 \) by \( -3q \):
\[
10 \times -3q = -30q
\]

3. Multiply \( 10 \) by \( 6 \):
\[
10 \times 6 = 60
\]

Now, combine all these results:
\[
10(2p - 3q + 6) = 20p - 30q + 60
\]

So the equivalent expression is:
\[
20p - 30q + 60
\]

Use the distributive property to write an equivalent expression.

2(f + 5g)

To use the distributive property on the expression \( 2(f + 5g) \), you'll need to multiply each term inside the parentheses by \( 2 \).

Here are the steps:

1. Multiply \( 2 \) by \( f \):
\[
2 \times f = 2f
\]

2. Multiply \( 2 \) by \( 5g \):
\[
2 \times 5g = 10g
\]

Now, combine these results:
\[
2(f + 5g) = 2f + 10g
\]

So, the equivalent expression is:
\[
2f + 10g
\]

Use the distributive property to write an equivalent expression.

10(m = 4n)

It seems there may be a typographical error in the expression you provided as \( 10(m = 4n) \). The equation \( m = 4n \) is not something that can be distributed; it is an equality.

If your intention was to use the distributive property with another expression involving \( m \) and \( n \), please clarify or correct it.

If you meant to use an expression like \( 10(m + 4n) \), you would proceed as follows:

Using the distributive property on \( 10(m + 4n) \):

1. Multiply \( 10 \) by \( m \):
\[
10 \times m = 10m
\]

2. Multiply \( 10 \) by \( 4n \):
\[
10 \times 4n = 40n
\]

Now, combine these results:
\[
10(m + 4n) = 10m + 40n
\]

So, the equivalent expression for \( 10(m + 4n) \) would be:
\[
10m + 40n
\]

If you meant something different, please let me know!

Use the distributive property to write an equivalent expression.

2(3x - 7y + 3)

To use the distributive property on the expression \( 2(3x - 7y + 3) \), you will multiply each term inside the parentheses by \( 2 \).

Here are the steps:

1. Multiply \( 2 \) by \( 3x \):
\[
2 \times 3x = 6x
\]

2. Multiply \( 2 \) by \( -7y \):
\[
2 \times -7y = -14y
\]

3. Multiply \( 2 \) by \( 3 \):
\[
2 \times 3 = 6
\]

Now, combine these results:
\[
2(3x - 7y + 3) = 6x - 14y + 6
\]

So the equivalent expression is:
\[
6x - 14y + 6
\]

Use the distributive property to write an equivalent expression.

8(10x + 10y - 3)

To use the distributive property on the expression \( 8(10x + 10y - 3) \), you will multiply each term inside the parentheses by \( 8 \).

Here are the steps:

1. Multiply \( 8 \) by \( 10x \):
\[
8 \times 10x = 80x
\]

2. Multiply \( 8 \) by \( 10y \):
\[
8 \times 10y = 80y
\]

3. Multiply \( 8 \) by \( -3 \):
\[
8 \times -3 = -24
\]

Now, combine these results:
\[
8(10x + 10y - 3) = 80x + 80y - 24
\]

So the equivalent expression is:
\[
80x + 80y - 24
\]

Use the distributive property to write an equivalent expression.

2(x - 2y + 8)

To use the distributive property on the expression \( 2(x - 2y + 8) \), you will multiply each term inside the parentheses by \( 2 \).

Here are the steps:

1. Multiply \( 2 \) by \( x \):
\[
2 \times x = 2x
\]

2. Multiply \( 2 \) by \( -2y \):
\[
2 \times -2y = -4y
\]

3. Multiply \( 2 \) by \( 8 \):
\[
2 \times 8 = 16
\]

Now, combine these results:
\[
2(x - 2y + 8) = 2x - 4y + 16
\]

So the equivalent expression is:
\[
2x - 4y + 16
\]

Enter the missing values in the area model to find 7(7m + 6)

____. +6
7 49m ___

To fill in the area model for the expression \( 7(7m + 6) \), we can break it down into parts.

1. We have \( 7 \) (the coefficient outside the parentheses) and two parts of the expression inside the parentheses: \( 7m \) and \( 6 \).
2. The area model can be represented as:

\[
\begin{array}{|c|c|}
\hline
7 & 6 \\
\hline
49m & \\
\hline
\end{array}
\]

3. Now, to find the missing value in the box along with \( 6 \):
- The value at the bottom left corner (which corresponds to \( 7 \times 7m \)) is \( 7 \times 7m = 49m \).
- The value at the bottom right corner should correspond to \( 7 \times 6 \), which is \( 42 \).

So, the completed area model will look like this:

\[
\begin{array}{|c|c|}
\hline
7 & 6 \\
\hline
49m & 42 \\
\hline
\end{array}
\]

The missing values are:

- **First blank:** \( 49m \)
- **Second blank:** \( 42 \)

Thus, the area model shows that \( 7(7m + 6) = 49m + 42 \).

According to the model above 7(7m + 6)

According to the area model constructed for \( 7(7m + 6) \), you have two parts represented by the areas:

1. The area corresponding to \( 7 \times 7m \), which is \( 49m \).
2. The area corresponding to \( 7 \times 6 \), which is \( 42 \).

So, when you combine these two areas, the expression becomes:

\[
49m + 42
\]

Therefore, the equation can be expressed as:
\[
7(7m + 6) = 49m + 42
\]

This shows that multiplying \( 7 \) by \( (7m + 6) \) results in \( 49m + 42 \).