(p%5E2%2B2).jpeg "(-p^2+4p-3)(p^2+2)")
Multiplying Polynomials: (-p^2 + 4p - 3)(p^2 + 2)
This article will walk through the steps of multiplying the polynomials (-p^2 + 4p - 3)(p^2 + 2) using the distributive property.
Step 1: Distribute the First Term
First, we distribute the -p² term from the first polynomial to each term in the second polynomial:
-p² * (p² + 2) = -p⁴ - 2p²
Step 2: Distribute the Second Term
Next, we distribute the 4p term from the first polynomial to each term in the second polynomial:
4p * (p² + 2) = 4p³ + 8p
Step 3: Distribute the Third Term
Finally, we distribute the -3 term from the first polynomial to each term in the second polynomial:
-3 * (p² + 2) = -3p² - 6
Step 4: Combine Like Terms
Now, we combine all the terms we've generated:
-p⁴ - 2p² + 4p³ + 8p - 3p² - 6
-p⁴ + 4p³ - 5p² + 8p - 6
Conclusion
Therefore, the product of the two polynomials (-p² + 4p - 3)(p² + 2) is -p⁴ + 4p³ - 5p² + 8p - 6.