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Select the correct answer.

Which expression is equivalent to the given polynomial expression?
[tex]\[ \left(9mn - 19m^4n\right) - \left(8m^2 + 12m^4n + 9mn\right) \][/tex]

A. [tex]\(-7m^4n + 18mn - 8m^2\)[/tex]

B. [tex]\(-31m^4n + 18mn - 8m^2\)[/tex]

C. [tex]\(-31m^4n - 8m^2\)[/tex]

D. [tex]\(-7m^4n + 8m^2\)[/tex]



Answer :

GinnyAnswer
First, let's start by carefully breaking down the given expression:

[tex]\[ (9mn - 19m^4n) - (8m^2 + 12m^4n + 9mn) \][/tex]

We need to distribute the negative sign across the second set of parentheses:

[tex]\[ = 9mn - 19m^4n - (8m^2 + 12m^4n + 9mn) \][/tex]
[tex]\[ = 9mn - 19m^4n - 8m^2 - 12m^4n - 9mn \][/tex]

Notice that [tex]\(9mn\)[/tex] and [tex]\(-9mn\)[/tex] cancel each other out:

[tex]\[ = -19m^4n - 8m^2 - 12m^4n \][/tex]

Combine like terms:

[tex]\[ = (-19m^4n - 12m^4n) - 8m^2 \][/tex]
[tex]\[ = -31m^4n - 8m^2 \][/tex]

Thus, the simplified expression is:

[tex]\[ m^2(-31m^2n - 8) \][/tex]

So, the correct answer is:

C. [tex]\(-31m^4n - 8m^2\)[/tex]

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