50 points!
what is the product of -2x^3 +x - 5 and x^3 - 3x - 4?

(a) show your work
(b) is the product of -2x^3 + x - 5 and x^3 - 3x - 4 equal to the product of x^3 - 3x - 4 and -2x^3 + x - 5? explain.

Step-by-step explanation:

a)

b)

When multiplying, the order doesn't matter: 2 × 3 = 3 × 2

This is referred to as "Commutative Property of Multiplication"

So, (-2x⁶+x-5)(x³-3x-4) = (x³-3x-4)(-2x⁶+x-5)

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

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.