Use the box method to distribute and simplify left parenthesis, minus, 3, x, plus, 4, right parenthesis, left parenthesis, 3, x, minus, 5, right parenthesis, .(−3x+4)(3x−5). Drag and drop the terms to the correct locations of the table.

Question

left parenthesis(minus−3, x3xplus+44right parenthesis)left parenthesis(3, x3xminus−55right parenthesis)
minus−3, x3x 44
3, x3x minus, 9, x, squared−9x
2
12, x12x
minus−55 15, x15x minus, 20−20
Correct! Now write the simplified answer in the box below.

Answer 1

To distribute and simplify \((-3x + 4)(3x - 5)\) using the box method, we can use the following table:

| | \(3x\) | \(-5\) | |----------|---------------|--------------| | \(-3x\) | \(-9x^2\) | \(15x\) | | \(4\) | \(12x\) | \(-20\) |

Now, let's fill in the box:

• For the top left cell: \(-3x \cdot 3x = -9x^2\)
• For the top right cell: \(-3x \cdot -5 = 15x\)
• For the bottom left cell: \(4 \cdot 3x = 12x\)
• For the bottom right cell: \(4 \cdot -5 = -20\)

Next, we sum the terms:

• The \(x^2\) term: \(-9x^2\)
• The \(x\) terms: \(15x + 12x = 27x\)
• The constant term: \(-20\)

Putting it all together, the simplified expression is:

\[ -9x^2 + 27x - 20 \]

So, the final answer is:

\(-9x^2 + 27x - 20\)

Answer 2

3x times -x
3x times -4
-x times -4
-4 times -4

Answer 3

To calculate the products you've mentioned, we can distribute each term accordingly:

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

2. \(3x \cdot -4\): \[ 3x \cdot -4 = -12x \]

3. \(-x \cdot -4\): \[ -x \cdot -4 = 4x \]

4. \(-4 \cdot -4\): \[ -4 \cdot -4 = 16 \]

Now if you would like to summarize these results, you get:

• \(3x \cdot -x = -3x^2\)
• \(3x \cdot -4 = -12x\)
• \(-x \cdot -4 = 4x\)
• \(-4 \cdot -4 = 16\)

If you want to combine the like terms from the \(x\) products:

\[ -12x + 4x = -8x \]

Putting it all together, the total result can be expressed as:

\[ -3x^2 - 8x + 16 \]

If needed, please let me know how you'd like to proceed further!

Answer 4

Use the box method to distribute and simplify left parenthesis, 3, x, minus, 4, right parenthesis, left parenthesis, minus, x, minus, 4, right parenthesis, .(3x−4)(−x−4). Drag and drop the terms to the correct locations of the table.
left parenthesis(3, x3xminus−44right parenthesis)left parenthesis(minus−xxminus−44right parenthesis)
3, x3x minus−44
minus−xx minus, 3, x, squared−3x
2
4, x4x
minus−44 minus, 12, x−12x 1616
Correct! Now write the simplified answer in the box below.

Answer 5

To distribute and simplify \((3x - 4)(-x - 4)\) using the box method, we can set up the table as follows:

| | \(-x\) | \(-4\) | |----------|--------------|--------------| | \(3x\) | \(-3x^2\) | \(-12x\) | | \(-4\) | \(4x\) | \(16\) |

Now let’s fill in the box:

1. For the top left cell: \[ 3x \cdot -x = -3x^2 \]

2. For the top right cell: \[ 3x \cdot -4 = -12x \]

3. For the bottom left cell: \[ -4 \cdot -x = 4x \]

4. For the bottom right cell: \[ -4 \cdot -4 = 16 \]

Next, we sum the terms from the table:

• The quadratic term is: \(-3x^2\)
• The linear terms are: \(-12x + 4x = -8x\)
• The constant term is: \(16\)

Putting it all together, the simplified expression is:

\[ -3x^2 - 8x + 16 \]

So, the final simplified answer is:

\(-3x^2 - 8x + 16\)

Answer 6

-x times -2x^2
-5x times -x
-2 times -2x^2
-2 times -5x

Answer 7

Let's compute the products you've provided:

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

2. \(-5x \cdot -x\): \[ -5x \cdot -x = 5x^2 \]

3. \(-2 \cdot -2x^2\): \[ -2 \cdot -2x^2 = 4x^2 \]

4. \(-2 \cdot -5x\): \[ -2 \cdot -5x = 10x \]

Now, let's summarize the results:

• \(-x \cdot -2x^2 = 2x^3\)
• \(-5x \cdot -x = 5x^2\)
• \(-2 \cdot -2x^2 = 4x^2\)
• \(-2 \cdot -5x = 10x\)

If you want to combine the like terms:

The \(x^2\) terms: \[ 5x^2 + 4x^2 = 9x^2 \]

Combine all terms together: \[ 2x^3 + 9x^2 + 10x \]

So, the final result is:

\(2x^3 + 9x^2 + 10x\)

Answer 8

Use the box method to distribute and simplify left parenthesis, 5, plus, 6, x, right parenthesis, left parenthesis, 2, x, squared, minus, 3, x, cubed, plus, 3, x, plus, 3, right parenthesis, .(5+6x)(2x
2
−3x
3
+3x+3). Drag and drop the terms to the correct locations of the table.
left parenthesis(55plus+6, x6xright parenthesis)left parenthesis(2, x, squared2x
2
minus−3, x, cubed3x
3
plus+3, x3xplus+33right parenthesis)
2, x, squared2x
2
minus−3, x, cubed3x
3
3, x3x 33
55
6, x6x

Answer 9

To distribute and simplify \((5 + 6x)(2x^2 - 3x^3 + 3x + 3)\) using the box method, we will set up the table as follows:

Table Setup:

| | \(2x^2\) | \(-3x^3\) | \(3x\) | \(3\) | |------------|------------|-------------|---------|-----------| | \(5\) | \(10x^2\) | \(-15x^3\) | \(15x\) | \(15\) | | \(6x\) | \(12x^3\) | \(-18x^4\) | \(18x^2\) | \(18x\) |

Now, let's compute each term in the box:

1. Top Row

   • For \(5 \cdot 2x^2\): \[ 5 \cdot 2x^2 = 10x^2 \]
   • For \(5 \cdot -3x^3\): \[ 5 \cdot -3x^3 = -15x^3 \]
   • For \(5 \cdot 3x\): \[ 5 \cdot 3x = 15x \]
   • For \(5 \cdot 3\): \[ 5 \cdot 3 = 15 \]

2. Bottom Row

   • For \(6x \cdot 2x^2\): \[ 6x \cdot 2x^2 = 12x^3 \]
   • For \(6x \cdot -3x^3\): \[ 6x \cdot -3x^3 = -18x^4 \]
   • For \(6x \cdot 3x\): \[ 6x \cdot 3x = 18x^2 \]
   • For \(6x \cdot 3\): \[ 6x \cdot 3 = 18x \]

Results in Each Cell of the Box:

| | \(2x^2\) | \(-3x^3\) | \(3x\) | \(3\) | |---------------|-----------------|-----------------|----------------|---------------| | \(5\) | \(10x^2\) | \(-15x^3\) | \(15x\) | \(15\) | | \(6x\) | \(12x^3\) | \(-18x^4\) | \(18x^2\) | \(18x\) |

Combine Like Terms:

Now let's combine all the terms from the box:

• \(x^4\) terms: \[ -18x^4 \]

• \(x^3\) terms: \[ -15x^3 + 12x^3 = -3x^3 \]

• \(x^2\) terms: \[ 10x^2 + 18x^2 = 28x^2 \]

• \(x\) terms: \[ 15x + 18x = 33x \]

• Constant term: \[ 15 \]

Final Simplified Expression:

Putting it all together, the final expression is: \[ -18x^4 - 3x^3 + 28x^2 + 33x + 15 \]

So, the simplified answer is:

\[ \boxed{-18x^4 - 3x^3 + 28x^2 + 33x + 15} \]

Answer 10

Find the sum of 8, x, minus, 28x−2 and minus, 3, x, squared, minus, 7−3x
2
−7

Answer 11

To find the sum of \(8x - 28x - 2\) and \(-3x^2 - 7\), we will first combine these expressions.

Step 1: Combine the terms

The expressions can be combined in the following way:

\[ (8x - 28x - 2) + (-3x^2 - 7) \]

Step 2: Simplify the first expression

Let's simplify \(8x - 28x - 2\):

1. Combine the \(x\) terms: \[ 8x - 28x = -20x \]
2. The constant term remains \(-2\).

So the first expression simplifies to: \[ -20x - 2 \]

Step 3: Combine with the second expression

Now, we will add the simplified expression to \(-3x^2 - 7\):

\[ (-20x - 2) + (-3x^2 - 7) \]

Step 4: Combine like terms

Combine the terms:

• The quadratic term is \(-3x^2\).
• The linear term is \(-20x\).
• The constant terms are \(-2 - 7\): \[ -2 - 7 = -9 \]

Final Result

Putting it all together, we get:

\[ -3x^2 - 20x - 9 \]

Thus, the sum is:

\[ \boxed{-3x^2 - 20x - 9} \]