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

Answer 1

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 2

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

Answer 3

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 4

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

Answer 5

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 6

Wrong After 2x^2 everything is positve try again

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!