(3m^3+m^2-2m-5)(m^2-5m-6)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (3m^3 + m^2 - 2m - 5)(m^2 - 5m - 6)

This article will guide you through expanding the given expression: (3m^3 + m^2 - 2m - 5)(m^2 - 5m - 6). We will achieve this by using the distributive property and combining like terms.

Expanding the Expression

1. Distribute the first term of the first polynomial: We start by multiplying each term of the second polynomial by 3m^3:

   3m^3(m^2 - 5m - 6) = 3m^5 - 15m^4 - 18m^3
   

2. Distribute the second term of the first polynomial: Next, we multiply each term of the second polynomial by m^2:

   m^2(m^2 - 5m - 6) = m^4 - 5m^3 - 6m^2 
   

3. Distribute the third term of the first polynomial: We then multiply each term of the second polynomial by -2m:

   -2m(m^2 - 5m - 6) = -2m^3 + 10m^2 + 12m 
   

4. Distribute the fourth term of the first polynomial: Finally, we multiply each term of the second polynomial by -5:

   -5(m^2 - 5m - 6) = -5m^2 + 25m + 30
   

Combining Like Terms

Now, we add all the terms we got from the distribution steps. Remember to combine terms with the same variable and exponent:

3m^5 - 15m^4 - 18m^3 + m^4 - 5m^3 - 6m^2 - 2m^3 + 10m^2 + 12m - 5m^2 + 25m + 30

Combining like terms, we get:

3m^5 - 14m^4 - 25m^3 - m^2 + 37m + 30

Conclusion

Therefore, the expanded form of the expression (3m^3 + m^2 - 2m - 5)(m^2 - 5m - 6) is 3m^5 - 14m^4 - 25m^3 - m^2 + 37m + 30. This process involved the distributive property and the combination of like terms.