what is the value of the expression when n = 3? -2n(5 + n - 8 - 3n) 12 24 42 54

Explanation:

Step1: Simplify the expression inside the parentheses

First, combine like - terms in (5 + n-8 - 3n): [ \begin{align*} 5 + n-8 - 3n&=(5 - 8)+(n-3n)\ &=-3 - 2n \end{align*} ] So the original expression (-2n(5 + n-8 - 3n)) becomes (-2n(-3 - 2n)).

Step2: Expand the expression

Use the distributive property (a(b + c)=ab+ac), where (a=-2n), (b = - 3), and (c=-2n): [ \begin{align*} -2n(-3 - 2n)&=(-2n)\times(-3)+(-2n)\times(-2n)\ &=6n + 4n^{2} \end{align*} ]

Step3: Substitute (n = 3) into the expanded expression

When (n = 3), we have: [ \begin{align*} 6n+4n^{2}&=6\times3+4\times3^{2}\ &=18 + 4\times9\ &=18+36\ &=54 \end{align*} ]

Answer:

D. 54