Distribute x, left parenthesis, minus, 3, x, plus, 2, right parenthesis, .x(−3x+2).

Answer 1

To distribute \( x \) in the expression \( x(-3x + 2) \), you will multiply \( x \) by each term inside the parentheses.

Here’s how it’s done step-by-step:

1. Multiply \( x \) by \(-3x\): \[ x \cdot (-3x) = -3x^2 \]

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

Now, combine the results of both multiplications:

\[ x(-3x + 2) = -3x^2 + 2x \]

Thus, the final expression is:

\[ -3x^2 + 2x \]

Answer 2

Distribute minus, 7, left parenthesis, minus, 9, x, squared, plus, 3, x, right parenthesis, .−7(−9x
2
+3x).

Answer 3

To distribute \(-7\) in the expression \(-7(-9x^2 + 3x)\), you will multiply \(-7\) by each term inside the parentheses.

Here’s how it’s done step-by-step:

1. Multiply \(-7\) by \(-9x^2\): \[ -7 \cdot (-9x^2) = 63x^2 \]

2. Multiply \(-7\) by \(3x\): \[ -7 \cdot 3x = -21x \]

Now, combine the results of both multiplications:

\[ -7(-9x^2 + 3x) = 63x^2 - 21x \]

Thus, the final expression is:

\[ 63x^2 - 21x \]

Answer 4

Multiply.
x, left parenthesis, minus, 8, x, squared, plus, 3, right parenthesis
x(−8x
2
+3)

Answer 5

To multiply \( x \) and the expression \( (-8x^2 + 3) \), you will distribute \( x \) to each term inside the parentheses.

Here’s how it’s done step-by-step:

1. Multiply \( x \) by \(-8x^2\): \[ x \cdot (-8x^2) = -8x^{3} \]

2. Multiply \( x \) by \( 3 \): \[ x \cdot 3 = 3x \]

Now, combine the results of both multiplications:

\[ x(-8x^2 + 3) = -8x^{3} + 3x \]

Thus, the final expression is:

\[ -8x^{3} + 3x \]

Answer 6

Multiply
9x(6x
2
+4)

Answer 7

To multiply \( 9x \) by the expression \( (6x^2 + 4) \), you will distribute \( 9x \) to each term inside the parentheses.

Here’s how it’s done step-by-step:

1. Multiply \( 9x \) by \( 6x^2 \): \[ 9x \cdot 6x^2 = 54x^{3} \]

2. Multiply \( 9x \) by \( 4 \): \[ 9x \cdot 4 = 36x \]

Now, combine the results of both multiplications:

\[ 9x(6x^2 + 4) = 54x^{3} + 36x \]

Thus, the final expression is:

\[ 54x^{3} + 36x \]

Answer 8

Use the box method to distribute and simplify left parenthesis, 2, x, minus, 5, right parenthesis, left parenthesis, 3, x, plus, 3, right parenthesis, .(2x−5)(3x+3). Drag and drop the terms to the correct locations of the table.
left parenthesis(2, x2xminus−55right parenthesis)left parenthesis(3, x3xplus+33right parenthesis)
2, x2x minus−55
3, x3x
33

Answer 9

To use the box method for distributing and simplifying the expression \((2x - 5)(3x + 3)\), we can set up a box (or grid) with the terms from each factor.

Step 1: Set up the box

Create a box with two rows and two columns:

| | \(3x\) | \(3\) | |------------|--------|--------| | \(2x\) | | | | \(-5\) | | |

Step 2: Fill in the box

Now fill in each cell by multiplying the terms from the rows and columns:

1. First cell: \(2x \cdot 3x = 6x^2\)
2. Second cell: \(2x \cdot 3 = 6x\)
3. Third cell: \(-5 \cdot 3x = -15x\)
4. Fourth cell: \(-5 \cdot 3 = -15\)

The completed box will look like this:

| | \(3x\) | \(3\) | |------------|--------|--------| | \(2x\) | \(6x^2\) | \(6x\) | | \(-5\) | \(-15x\) | \(-15\) |

Step 3: Combine like terms

Now, add together all the terms from the box:

• \(6x^2\)
• \(6x - 15x = -9x\)
• \(-15\)

Final Expression

Combining these terms, we have:

\[ 6x^2 - 9x - 15 \]

Thus, the simplified expression for \((2x - 5)(3x + 3)\) is:

\[ 6x^2 - 9x - 15 \]

Answer 10

Use the box method to distribute and simplify left parenthesis, 6, x, plus, 6, right parenthesis, left parenthesis, 2, x, plus, 2, right parenthesis, .(6x+6)(2x+2). Drag and drop the terms to the correct locations of the table.
left parenthesis(6, x6xplus+66right parenthesis)left parenthesis(2, x2xplus+22right parenthesis)
6, x6x 66
2, x2x 12, x, squared12x
2
12, x12x
22 12, x12x 1212
Correct! Now write the simplified answer in the box below.

Answer 11

To use the box method for distributing and simplifying the expression \((6x + 6)(2x + 2)\), we can set up a box (or grid) with the terms from each factor.

Step 1: Set up the box

Create a box with two rows and two columns:

| | \(2x\) | \(2\) | |------------|--------|--------| | \(6x\) | | | | \(6\) | | |

Step 2: Fill in the box

Now fill in each cell by multiplying the terms from the rows and columns:

1. First cell: \(6x \cdot 2x = 12x^2\)
2. Second cell: \(6x \cdot 2 = 12x\)
3. Third cell: \(6 \cdot 2x = 12x\)
4. Fourth cell: \(6 \cdot 2 = 12\)

The completed box will look like this:

| | \(2x\) | \(2\) | |------------|--------|--------| | \(6x\) | \(12x^2\) | \(12x\) | | \(6\) | \(12x\) | \(12\) |

Step 3: Combine like terms

Now, add together all the terms from the box:

• \(12x^2\)
• \(12x + 12x = 24x\)
• \(12\)

Final Expression

Combining these terms, we have:

\[ 12x^2 + 24x + 12 \]

Thus, the simplified expression for \((6x + 6)(2x + 2)\) is:

\[ 12x^2 + 24x + 12 \]