Use the distributive property to write an equivalent expression.

Question

9(4f - 4g + 6)

Answer 1

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: \[ 36f - 36g + 54 \]

Answer 2

Use the distributive property to write an equivalent expression.

2(r + 7)

Answer 3

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: \[ 2r + 14 \]

Answer 4

Use the distributive property to write an equivalent expression.

10(2p - 3q + 6)

Answer 5

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: \[ 20p - 30q + 60 \]

Answer 6

Use the distributive property to write an equivalent expression.

2(f + 5g)

Answer 7

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: \[ 2f + 10g \]

Answer 8

Use the distributive property to write an equivalent expression.

10(m = 4n)

Answer 9

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!

Answer 10

Use the distributive property to write an equivalent expression.

2(3x - 7y + 3)

Answer 11

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: \[ 6x - 14y + 6 \]

Answer 12

Use the distributive property to write an equivalent expression.

8(10x + 10y - 3)

Answer 13

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: \[ 80x + 80y - 24 \]

Answer 14

Use the distributive property to write an equivalent expression.

2(x - 2y + 8)

Answer 15

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: \[ 2x - 4y + 16 \]

Answer 16

Enter the missing values in the area model to find 7(7m + 6)
____. +6
7 49m ___

Answer 17

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 \( 7(7m + 6) = 49m + 42 \).

Answer 18

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

Answer 19

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 \( 49m + 42 \).