Question

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

Answer 1

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

Here's how it's done step by step:

1. **First terms:** Multiply the first terms in each binomial:
\[
x \cdot x = x^2
\]

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

3. **Inner terms:** Multiply the inner terms:
\[
2 \cdot x = 2x
\]

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

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

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

So, the final result of multiplying the polynomial expressions \((x + 2)(x - 4)\) is:
\[
\boxed{x^2 - 2x - 8}
\]