Which polynomial identity will prove that 35 = 27 + 8? a. difference of squares b. difference of cubes c. sum of cubes d. square of a binomial

Option c that is sum of cubes will prove 35 = 27 + 8

Step-by-step explanation:

We have been given:

35 = 27 + 8

On the right hand side of the above equation we have been given two numbers

27 which is cube of 3

And 8 which is cube of 2

we can clearly see the right hand side of the above equation is sum of the cubes.

Hence, option c that is sum of cubes will prove 35 = 27 + 8

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for