Question

Преобразуйте в многочлен выражения: -(v-5)^3-(v+2)(v+3)

Answer 1

-(v-5)³-(v+2)(v+3)=-(v³-125)-(v²+3v+2v+6)=-v³-125-v²-5v-6=-v³-v²-5v-131

Answer 2

Converting the Expressions to Polynomial Form

To convert the given expressions into polynomial form, we'll start by expanding each expression separately and then combining them.

1. Expanding -(v-5)^3: - The expression -(v-5)^3 can be expanded using the binomial theorem, which states that (a - b)^n = Σ(n choose k) * a^(n-k) * (-b)^k, where Σ is the summation symbol and k ranges from 0 to n.

The expansion of -(v-5)^3 is: ``` -(v-5)^3 = -v^3 + 15v^2 - 75v + 125 ```

2. Expanding -(v+2)(v+3): - The expression -(v+2)(v+3) can be expanded using the distributive property of multiplication over addition.

The expansion of -(v+2)(v+3) is: ``` -(v+2)(v+3) = -v^2 - 5v - 6 ```

Combining the Polynomial Expressions

Now, we can combine the expanded polynomial expressions:

   -v^3 + 15v^2 - 75v + 125 -v^2 - 5v - 6
   

Simplifying the combined polynomial expression:

   -v^3 + 15v^2 - 75v + 125 -v^2 - 5v - 6 = -v^3 + 14v^2 - 80v + 119
   

So, the combined polynomial expression is: ``` -v^3 + 14v^2 - 80v + 119 ```