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Multiply the polynomial expression (x+2)(x−4)

.(2 points)

3 answers

To multiply the polynomial expression \((x + 2)(x - 4)\), we can use the distributive property (also known as the FOIL method for binomials).

  1. First: Multiply the first terms:
    \(x \cdot x = x^2\)

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

  3. Inner: Multiply the inner terms:
    \(2 \cdot x = 2x\)

  4. Last: Multiply the last terms:
    \(2 \cdot (-4) = -8\)

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

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

Thus, the product of the polynomial expression \((x + 2)(x - 4)\) is:
\[ \boxed{x^2 - 2x - 8} \]

Multiply to simplify the polynomial expression (r−1)(r2−2r+3)
.(2 points)

To multiply and simplify the polynomial expression \((r - 1)(r^2 - 2r + 3)\), we can use the distributive property.

  1. Distribute \(r\) to each term in the second polynomial: \[ r \cdot r^2 = r^3 \] \[ r \cdot (-2r) = -2r^2 \] \[ r \cdot 3 = 3r \]

  2. Distribute \(-1\) to each term in the second polynomial: \[ -1 \cdot r^2 = -r^2 \] \[ -1 \cdot (-2r) = 2r \] \[ -1 \cdot 3 = -3 \]

  3. Now, combine all these results: \[ r^3 - 2r^2 + 3r - r^2 + 2r - 3 \]

  4. Combine like terms:

    • Combine \( -2r^2 \) and \( -r^2 \):
      \(-2r^2 - r^2 = -3r^2\)

    • Combine \( 3r \) and \( 2r \):
      \(3r + 2r = 5r\)

    So, the expression becomes: \[ r^3 - 3r^2 + 5r - 3 \]

Thus, the simplified product of the polynomial expression \((r - 1)(r^2 - 2r + 3)\) is: \[ \boxed{r^3 - 3r^2 + 5r - 3} \]