(-p^2+4p-3)(p^2+2)

Jasonbradley

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Jun 16, 2024

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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.