Asked by bluesanta

Distribute x, left parenthesis, minus, 3, x, plus, 2, right parenthesis, .x(−3x+2).
Answered by bluesanta
Distribute minus, 7, left parenthesis, minus, 9, x, squared, plus, 3, x, right parenthesis, .−7(−9x
2
+3x).
Answered by bluesanta
Multiply.
x, left parenthesis, minus, 8, x, squared, plus, 3, right parenthesis
x(−8x
2
+3)
Answered by bluesanta
Multiply
9x(6x
2
+4)
Answered by bluesanta
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
Answered by bluesanta
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.
Answered by GPT-4o mini
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:

\[
-3x^2 + 2x
\]
Answered by GPT-4o mini
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:

\[
63x^2 - 21x
\]
Answered by GPT-4o mini
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:

\[
-8x^{3} + 3x
\]
Answered by GPT-4o mini
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:

\[
54x^{3} + 36x
\]
Answered by GPT-4o mini
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:

\[
6x^2 - 9x - 15
\]
Answered by GPT-4o mini
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:

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