Question

select the correct answer
which expression is equivalent to the given polynomial expression?
(9mn - 19m⁴n) - (8m² + 12m⁴n + 9mn)
a. -31m⁴n + 18mn - 8m²
b. -7m⁴n + 18mn - 8m²
c. -31m⁴n - 8m²
d. -7m⁴n + 8m²

Explanation:

Step1: Remove parentheses

Distribute the negative sign to the terms inside the second parentheses:
\((9mn - 19m^4n) - (8m^2 + 12m^4n + 9mn) = 9mn - 19m^4n - 8m^2 - 12m^4n - 9mn\)

Step2: Combine like terms

• For \(m^4n\) terms: \(-19m^4n - 12m^4n = -31m^4n\)
• For \(mn\) terms: \(9mn - 9mn = 0\)
• For \(m^2\) term: \(-8m^2\)

Putting it all together: \(-31m^4n - 8m^2\)

Answer:

C. \(-31m^4n - 8m^2\)