Question

Use the following multiplication problem to show how multiplying polynomials is a closed system.

(x2−1)(−2x+5)




say it like how a 8th grader would and easy to copy and paste

Answer 1

Sure! Let's look at the multiplication problem \((x^2 - 1)(-2x + 5)\) and see how multiplying polynomials works in a closed system.

1. **Write the Expression:**
We start with \((x^2 - 1)(-2x + 5)\).

2. **Use the Distributive Property:**
We will distribute each term in the first polynomial \((x^2 - 1)\) to each term in the second polynomial \((-2x + 5)\).

- First, distribute \(x^2\) to both terms in \((-2x + 5)\):
- \(x^2 \cdot -2x = -2x^3\)
- \(x^2 \cdot 5 = 5x^2\)

- Next, distribute \(-1\) to both terms in \((-2x + 5)\):
- \(-1 \cdot -2x = 2x\)
- \(-1 \cdot 5 = -5\)

3. **Combine All the Terms:**
Now, we bring all those terms together:
\(-2x^3 + 5x^2 + 2x - 5\)

4. **Final Result:**
So, when we multiply, we get:
\(-2x^3 + 5x^2 + 2x - 5\)

### Conclusion:
This shows that when we multiply two polynomials, we still end up with another polynomial, which is why it's called a closed system. You can keep multiplying polynomials, and you won't get anything other than another polynomial!