Question

Use the distributive property to rewrite the polynomial (x+8)*(x-2)

Answer 1

it has to all be addition in the final answer

Answer 2

rewrite the expression 3x*9x+3) using the distributive property

Answer 3

rewrite the expression 3x*(x+3) using the distributive property

Answer 4

find the product of the polynomials (2x+1)*(x-4)

Answer 5

it has to be positive

Answer 6

To use the distributive property to rewrite the polynomial \((x + 8)(x - 2)\), we distribute each term in the first parenthesis by each term in the second parenthesis. Here are the steps:

1. Distribute \(x\) in \((x + 8)\):
\[
x \cdot (x - 2) = x^2 - 2x
\]

2. Distribute \(8\) in \((x + 8)\):
\[
8 \cdot (x - 2) = 8x - 16
\]

Now, combine all the terms:
\[
x^2 - 2x + 8x - 16
\]

Next, combine like terms:
\[
x^2 + 6x - 16
\]

Thus, the polynomial \((x + 8)(x - 2)\) rewritten using the distributive property is:
\[
\boxed{x^2 + 6x - 16}
\]

Answer 7

Sure! When combining terms, we can rewrite the expression using addition only. Here’s the process to ensure that we get the final answer in the requested form:

Starting from the original expression:
\[
(x + 8)(x - 2)
\]

Using the distributive property:
1. Distributing \(x\):
\[
x \cdot x + x \cdot (-2) = x^2 - 2x
\]

2. Distributing \(8\):
\[
8 \cdot x + 8 \cdot (-2) = 8x - 16
\]

Now, we combine all the terms:
\[
x^2 - 2x + 8x - 16
\]

Next, we can rewrite it to express it with all terms as addition:
\[
x^2 + 6x - 16
\]

Now, to explicitly have only addition, we rearrange \(-16\) as \(+ (-16)\):
\[
x^2 + 6x + (-16)
\]

Thus, the final expression using the distributive property and having all positive signs is:
\[
\boxed{x^2 + 6x + (-16)}
\]

Answer 8

To rewrite the expression \( 3x(9x + 3) \) using the distributive property, we distribute \( 3x \) to both terms inside the parentheses \( (9x + 3) \).

Here are the steps:

1. Distribute \( 3x \) to \( 9x \):
\[
3x \cdot 9x = 27x^2
\]

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

Now, combine the results:
\[
27x^2 + 9x
\]

So, the expression \( 3x(9x + 3) \) rewritten using the distributive property is:
\[
\boxed{27x^2 + 9x}
\]

Answer 9

To rewrite the expression \( 3x(x + 3) \) using the distributive property, we distribute \( 3x \) to both terms inside the parentheses \( (x + 3) \).

Here are the steps:

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

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

Now, combine the results:
\[
3x^2 + 9x
\]

So, the expression \( 3x(x + 3) \) rewritten using the distributive property is:
\[
\boxed{3x^2 + 9x}
\]

Answer 10

To find the product of the polynomials \((2x + 1)(x - 4)\), we can use the distributive property (also known as the FOIL method for binomials). Here are the steps:

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 of the results:
\[
2x^2 - 8x + x - 4
\]

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

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

Answer 11

To rewrite the expression \((2x + 1)(x - 4)\) such that all terms are expressed with positive signs, we will break it down through the distributive property and rearrange the final expression.

Starting with:
\[
(2x + 1)(x - 4)
\]

We will use the distributive property (FOIL method):

1. **First:**
\[
2x \cdot x = 2x^2
\]

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

3. **Inner:**
\[
1 \cdot x = 1x = x
\]

4. **Last:**
\[
1 \cdot (-4) = -4
\]

Combining these results, we have:
\[
2x^2 - 8x + x - 4
\]

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

To express this result in a form where all constants and coefficients are presented with addition, we can rewrite the negative terms as follows:
\[
2x^2 + (-7x) + (-4)
\]

This expression can be rewritten as:
\[
2x^2 + (-7)x + (-4)
\]

Thus, if we want to keep the expression with positive signs while indicating the negatives explicitly, we can say the final product can be represented as:
\[
\boxed{2x^2 + (-7x) + (-4)}
\]

However, if your intention is to have strictly positive coefficients (which would change the expression itself), we cannot simply convert negative coefficients to positive without altering the expression.

If you are looking for a positive form without changing the meaning, you might want to clarify further, as the polynomial inherently contains those negatives based on multiplication.