What is the equivalent of (n+4)^3 ? A. n^3 +64
B. n^3 +6n² +24n+32
C. n^3+12n^2 + 48n + 64
D. n^3 +12n^2 +48n +32
E. n^3 +24n^2 +48n+64

C)

Step-by-step explanation:

(n+4)(n+4) = n² + 4n + 4n + 16

this can be simplified to get:

n² + 8n + 16

now multiply the above by (n+4)

(n²+8n+16)(n+4) by multiplying each of the three terms in the first set of parentheses by each of the two terms in the second set to get:

n³ + 4n² + 8n² + 32n + 16n + 64  [Now look to combine 'like terms']

n³ + 12n² + 48n + 64 [this is option C]

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.