Which of the following is equivalent to the given expression?

The correct answer is:

1. The given expression is a Cubic expression wherein the variable with the highest power is 3. We will simplify the given expression to find the correct solution.
2. Options A & Option B has variables with power 5 which is more than 3. Therefore, Option A & Option B can not be the correct Options.
Step-by-step solution:-
(x³ + x) + (x² -x) = x³ + x + x² – x -------------------------- (Opening the brackets)
= x³ + x² + x - x -------------------------- (Rearranging the variables)
= x³ + x² + 0
= x³ + x²
Final Answer:-
Option C i.e. x³ + x² is the correct Option.
Note:-
Alternatively, we can substitute any number in place of x and find the solution of the given expression and the 4 options.
Eg. Substituting x = 1, we get-
(x³ + x) + (x² -x) = 1³ + 1 + 1² - 1 -------------------------- (Opening the brackets)
= 1 + 1 + 1 - 1 -------------------------- (Rearranging the variables)
= 2
Option A = x⁵ - x²
= 1⁵ - 1²
= 1 - 1
= 0
Option B = x⁵ - x⁴ + x³ - x²
= 1⁵ - 1⁴ + 1³ - 1²
= 1 - 1 + 1 - 1
= 0
Option C = x³ + x²
= 1³ + 1²
= 1 + 1
= 2
Option D = x³ + x² + 2x
= 1³ + 1² + 2(1)
= 1 + 1 + 2
= 4
Hence, Option C is the correct Option.