Question

find the product. simplify your answer.
$(n - 3)(2n^2 - 3n + 2)$

Explanation:

Step1: Distribute \( n \)

Multiply \( n \) by each term in \( 2n^2 - 3n + 2 \):
\( n \cdot 2n^2 = 2n^3 \), \( n \cdot (-3n) = -3n^2 \), \( n \cdot 2 = 2n \)
So, \( n(2n^2 - 3n + 2) = 2n^3 - 3n^2 + 2n \)

Step2: Distribute \( -3 \)

Multiply \( -3 \) by each term in \( 2n^2 - 3n + 2 \):
\( -3 \cdot 2n^2 = -6n^2 \), \( -3 \cdot (-3n) = 9n \), \( -3 \cdot 2 = -6 \)
So, \( -3(2n^2 - 3n + 2) = -6n^2 + 9n - 6 \)

Step3: Combine like terms

Add the results from Step1 and Step2:
\( (2n^3 - 3n^2 + 2n) + (-6n^2 + 9n - 6) \)
Combine \( -3n^2 \) and \( -6n^2 \): \( -9n^2 \)
Combine \( 2n \) and \( 9n \): \( 11n \)
So, \( 2n^3 - 9n^2 + 11n - 6 \)

Answer:

\( 2n^3 - 9n^2 + 11n - 6 \)