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

.(2 points)
?x2+?x+?

5 answers

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: \(x^2 + 6x - 16\)

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

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:

\[ 3x^2 + 9x \]

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

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: \(2x^2 - 7x - 4\)