Question

use the Distributive Property to rewrite the polynomial (x+8)(x−2)

Answer 1

Rewrite the expression 3x(x + 3)
using the Distributive Property.

Answer 2

Find the product of the polynomials (2x+1)(x−4)

Answer 3

Wrong After 2x^2 everything is positve try again

Answer 4

To rewrite the polynomial \((x + 8)(x - 2)\) using the Distributive Property, you'll distribute each term in the first parenthesis by each term in the second parenthesis.

Here's how you do it step by step:

1. Distribute \(x\) to both terms in the second parenthesis:
\[
x \cdot (x - 2) = x^2 - 2x
\]

2. Distribute \(8\) to both terms in the second parenthesis:
\[
8 \cdot (x - 2) = 8x - 16
\]

3. Now combine the results from both distributions:
\[
x^2 - 2x + 8x - 16
\]

4. Combine like terms (\(-2x + 8x\)):
\[
x^2 + 6x - 16
\]

So, the polynomial \((x + 8)(x - 2)\) can be rewritten as:
\[
x^2 + 6x - 16
\]

Answer 5

To rewrite the expression \(3x(x + 3)\) using the Distributive Property, you'll distribute \(3x\) to each term inside the parentheses:

1. Distribute \(3x\) to the first term \(x\):
\[
3x \cdot x = 3x^2
\]

2. Distribute \(3x\) to the second term \(3\):
\[
3x \cdot 3 = 9x
\]

3. Combine the results from both distributions:
\[
3x^2 + 9x
\]

Thus, the expression \(3x(x + 3)\) can be rewritten as:
\[
3x^2 + 9x
\]

Answer 6

To find the product of the polynomials \((2x + 1)(x - 4)\), we will use the Distributive Property (also known as the FOIL method for binomials):

1. **First**: Multiply the first terms:
\[
2x \cdot x = 2x^2
\]

2. **Outer**: Multiply the outer terms:
\[
2x \cdot (-4) = -8x
\]

3. **Inner**: Multiply the inner terms:
\[
1 \cdot x = 1x = x
\]

4. **Last**: Multiply the last terms:
\[
1 \cdot (-4) = -4
\]

Now, combine all these results:
\[
2x^2 - 8x + x - 4
\]

Combine the like terms (\(-8x\) and \(x\)):
\[
2x^2 - 7x - 4
\]

Thus, the product of the polynomials \((2x + 1)(x - 4)\) is:
\[
2x^2 - 7x - 4
\]

Answer 7

Let's go through the multiplication of the polynomials \((2x + 1)(x - 4)\) step by step again:

Using the Distributive Property (or FOIL for binomials):

1. **First**: Multiply the first terms:
\[
2x \cdot x = 2x^2
\]

2. **Outer**: Multiply the outer terms:
\[
2x \cdot (-4) = -8x
\]

3. **Inner**: Multiply the inner terms:
\[
1 \cdot x = 1x = x
\]

4. **Last**: Multiply the last terms:
\[
1 \cdot (-4) = -4
\]

Now, combine all these results:
\[
2x^2 - 8x + x - 4
\]

Now, combine the like terms (\(-8x\) and \(x\)):
\[
2x^2 - 7x - 4
\]

So the product of the polynomials \((2x + 1)(x - 4)\) is:
\[
2x^2 - 7x - 4
\]

Thus, my previous calculation was indeed correct. The resulting polynomial contains both positive and negative terms based on the multiplication steps shown above. If you have a specific aspect about it that you'd like to clarify, please let me know!