Question

Use the Distributive Property to rewrite the polynomial (x+8)(x−2)
.(2 points)
?x2+?x+?

Answer 1

Rewrite the expression 3x(x + 3)
using the Distributive Property.(1 point)

Answer 2

Find the product of the polynomials (2x+1)(x−4)
.(2 points)
x2+
x+

Answer 3

To use the Distributive Property (also known as the FOIL method, when dealing with binomials) to rewrite the polynomial \((x + 8)(x - 2)\), we will multiply each term in the first binomial by each term in the second binomial.

1. **First**: \(x \cdot x = x^2\)
2. **Outer**: \(x \cdot (-2) = -2x\)
3. **Inner**: \(8 \cdot x = 8x\)
4. **Last**: \(8 \cdot (-2) = -16\)

Now, we will combine all these results together:

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

Next, we combine the like terms (\(-2x + 8x\)):

\[
x^2 + 6x - 16
\]

So, rewritten, the polynomial \((x + 8)(x - 2)\) is:

\[
x^2 + 6x - 16
\]

**Final answer:**
\(x^2 + 6x - 16\)

Answer 4

To rewrite the expression \(3x(x + 3)\) using the Distributive Property, you multiply \(3x\) by each term inside the parentheses:

1. **First Term**: \(3x \cdot x = 3x^2\)
2. **Second Term**: \(3x \cdot 3 = 9x\)

Now, we combine these results:

\[
3x(x + 3) = 3x^2 + 9x
\]

So, the expression rewritten using the Distributive Property is:

\[
3x^2 + 9x
\]

Answer 5

To find the product of the polynomials \((2x + 1)(x - 4)\), we will use the Distributive Property (or FOIL method).

1. **First**: \(2x \cdot x = 2x^2\)
2. **Outer**: \(2x \cdot (-4) = -8x\)
3. **Inner**: \(1 \cdot x = 1x\)
4. **Last**: \(1 \cdot (-4) = -4\)

Now, we combine these results:

\[
2x^2 - 8x + 1x - 4
\]

Next, we combine the like terms (\(-8x + 1x\)):

\[
2x^2 - 7x - 4
\]

So, the product of the polynomials \((2x + 1)(x - 4)\) is:

\[
2x^2 - 7x - 4
\]

**Final answer:**
\(2x^2 - 7x - 4\)