Question

HelloI need help with a problemSimplify the expressionv^3+125/v^2-25

Answer 1

We are given the following expression:

`(v^3+125)/(v^2-25)`

To simplify the expression we will factor the numerator and denominator. To factor the numerator we will use the following:

`(a^3+b^3)=(a+b)(a^2-ab+b^2)`

Applying the formula we get:

`(v^(3)+125)/(v^(2)-25)=((v+5)(v^2-5v+25))/(v^2-25)`

Now, we will factor the denominator using the following:

`(a^2-b^2)=(a+b)(a-b)`

Applying the rule we get:

`((v+5)(v^2-5v+25))/(v^2-25)=((v+5)(v^2-5v+25))/((v+5)(v-5))`

Now, we can cancel out the "v + 5", and we get:

`((v+5)(v^2-5v+25))/((v+5)(v-5))=(v^2-5v+25)/(v-5)`

and thus we get the simplified form of the expression.